If the corresponding angles of two triangles are equal, then they are always. State true or false and justify your answer. -Maths 9th

If the corresponding angles of two triangles are equal, then they are always. State true or false and justify your answer. -Maths 9th
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Solution   :-  False, because two equilateral triangles with sides 3 cm and 6 cm respectively have all angles equal, but the triangles are not congruent.
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Prove that if in two triangles,two angles and the included side of one triangle are equal to two angles and the included side of the other triangle,then two triangles are congruent. -Maths 9th

Description : Prove that if in two triangles,two angles and the included side of one triangle are equal to two angles and the included side of the other triangle,then two triangles are congruent. -Maths 9th

Last Answer : Solution :-

If the angles of a triangle are in the ratio 1 : 2 : 3, then find the ratio of the corresponding opposite sides. -Maths 9th

Description : If the angles of a triangle are in the ratio 1 : 2 : 3, then find the ratio of the corresponding opposite sides. -Maths 9th

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Is this statement true or falseTo prove triangles similar using the Side-Side-Side Similarity Theorem, you must first prove that corresponding angles are congruent?

Description : Is this statement true or falseTo prove triangles similar using the Side-Side-Side Similarity Theorem, you must first prove that corresponding angles are congruent?

Last Answer : Answers is the place to go to get the answers you need and to ask the questions you want

State whether the following statements are true or false ? Justify your answer. -Maths 9th

Description : State whether the following statements are true or false ? Justify your answer. -Maths 9th

Last Answer : (i) False, here √2 is an irrational number and 3 is a rational number, we know that when we divide irrational number by non-zero rational number it will always give an irrational number. (ii) False, ... in the form p/q, q ≠0. p,q both are integers and these numbers are called irrational numbers.

State whether the following statements are true or false ? Justify your answer. -Maths 9th

Description : State whether the following statements are true or false ? Justify your answer. -Maths 9th

Last Answer : (i) False, here √2 is an irrational number and 3 is a rational number, we know that when we divide irrational number by non-zero rational number it will always give an irrational number. (ii) False, ... in the form p/q, q ≠0. p,q both are integers and these numbers are called irrational numbers.

Write whether the following statements are true or false. Justify your answer. ’ -Maths 9th

Description : Write whether the following statements are true or false. Justify your answer. ’ -Maths 9th

Last Answer : (i) False, because a binomial has exactly two terms. (ii) False, because every polynomial is not a binomial . e.g., (a) 3x2 + 4x + 5 [polynomial but hot a binomial] (b) 3x2 + 5 [polynomial and also a binomial] (Hi ... = x4 + 2 + (-x4 + 4x3 + 2x) = 4x3 + 2x + 2 which is not a polynomial of degree 4.

Write whether the following statements are true or false? Justify your answer. -Maths 9th

Description : Write whether the following statements are true or false? Justify your answer. -Maths 9th

Last Answer : (i) False, since the ordinate of the point (3, 0) is zero. So, the point lies on X-axis. (ii) False, because in point (1, -1) x-coordinate is positive and y-coordinate is negative, so it lies ... -axis is 2 units. (v) True, because in a point (-1, 7) abscissa is negative and ordinate is positive.

Write whether the following statements are true or false. Justify your answer. ’ -Maths 9th

Description : Write whether the following statements are true or false. Justify your answer. ’ -Maths 9th

Last Answer : (i) False, because a binomial has exactly two terms. (ii) False, because every polynomial is not a binomial . e.g., (a) 3x2 + 4x + 5 [polynomial but hot a binomial] (b) 3x2 + 5 [polynomial and also a binomial] (Hi ... = x4 + 2 + (-x4 + 4x3 + 2x) = 4x3 + 2x + 2 which is not a polynomial of degree 4.

Write whether the following statements are true or false? Justify your answer. -Maths 9th

Description : Write whether the following statements are true or false? Justify your answer. -Maths 9th

Last Answer : (i) False, since the ordinate of the point (3, 0) is zero. So, the point lies on X-axis. (ii) False, because in point (1, -1) x-coordinate is positive and y-coordinate is negative, so it lies ... -axis is 2 units. (v) True, because in a point (-1, 7) abscissa is negative and ordinate is positive.

what- Two triangles are congruent if there is a way of writing a correspondence so that all of the corresponding sides and angles are?

Description : what- Two triangles are congruent if there is a way of writing a correspondence so that all of the corresponding sides and angles are?

Last Answer : i think its congruent

EF is the transversal to two parallel lines AB and CD. GM and HL are the bisector of the corresponding angles EGB and EHD.Prove that GL parallel to HL. -Maths 9th

Description : EF is the transversal to two parallel lines AB and CD. GM and HL are the bisector of the corresponding angles EGB and EHD.Prove that GL parallel to HL. -Maths 9th

Last Answer : AB || CD and a transversal EF intersects them ∴ ∠EGB = ∠GHD ( Corresponding Angles) ⇒ 2 ∠EGM = 2 ∠GHL ∵ GM and HL are the bisectors of ∠EGB and ∠EHD respectively. ⇒ ∠EGM = ∠GHL But these angles form a pair of equal corresponding angles for lines GM and HL and transversal EF. ∴ GM || HL.

EF is the transversal to two parallel lines AB and CD. GM and HL are the bisector of the corresponding angles EGB and EHD.Prove that GL parallel to HL. -Maths 9th

Description : EF is the transversal to two parallel lines AB and CD. GM and HL are the bisector of the corresponding angles EGB and EHD.Prove that GL parallel to HL. -Maths 9th

Last Answer : AB || CD and a transversal EF intersects them ∴ ∠EGB = ∠GHD ( Corresponding Angles) ⇒ 2 ∠EGM = 2 ∠GHL ∵ GM and HL are the bisectors of ∠EGB and ∠EHD respectively. ⇒ ∠EGM = ∠GHL But these angles form a pair of equal corresponding angles for lines GM and HL and transversal EF. ∴ GM || HL.

If a transversal intersects two parallel lines, prove that the bisectors of any pair of corresponding angles so formed are parallel. -Maths 9th

Description : If a transversal intersects two parallel lines, prove that the bisectors of any pair of corresponding angles so formed are parallel. -Maths 9th

Last Answer : Solution :-

‘If two sides and an angle of one triangle are equal to two sides and an angle of another triangle , then the two triangles must be congruent’. -Maths 9th

Description : ‘If two sides and an angle of one triangle are equal to two sides and an angle of another triangle , then the two triangles must be congruent’. -Maths 9th

Last Answer : No, because in the congruent rule, the two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle i.e., SAS rule.

‘If two sides and an angle of one triangle are equal to two sides and an angle of another triangle , then the two triangles must be congruent’. -Maths 9th

Description : ‘If two sides and an angle of one triangle are equal to two sides and an angle of another triangle , then the two triangles must be congruent’. -Maths 9th

Last Answer : No, because in the congruent rule, the two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle i.e., SAS rule.

State whether the following statements are True or false. Justify your answers. -Maths 9th

Description : State whether the following statements are True or false. Justify your answers. -Maths 9th

Last Answer : Solution :-

Is the product of two irrational numbers always irrational ? Justify your answer. -Maths 9th

Description : Is the product of two irrational numbers always irrational ? Justify your answer. -Maths 9th

Last Answer : Solution :- No, sometimes rational,sometimes irrational.

Prove that median of a triangle divides it into two triangles of equal area. -Maths 9th

Description : Prove that median of a triangle divides it into two triangles of equal area. -Maths 9th

Last Answer : Solution :-

Write the coordinates of a point on x-axis at a distance of 6 units from the origin in the positive direction of x-axis and then justify your answer. -Maths 9th

Description : Write the coordinates of a point on x-axis at a distance of 6 units from the origin in the positive direction of x-axis and then justify your answer. -Maths 9th

Last Answer : Solution :- As, any point on x-axis has coordinates (,)x0 where x is the distance from origin, so required coordinates are (6, 0).

If the medians of two equilateral triangles are in the ratio 3 : 2, then what is the ratio of their sides? -Maths 9th

Description : If the medians of two equilateral triangles are in the ratio 3 : 2, then what is the ratio of their sides? -Maths 9th

Last Answer : answer:

In Fig. 4.6, if ABC and ABD are equilateral triangles then find the coordinates of C and D. -Maths 9th

Description : In Fig. 4.6, if ABC and ABD are equilateral triangles then find the coordinates of C and D. -Maths 9th

Last Answer : Solution :-

If AB = PQ, BC = QR and AC = PR, then write the congruence relation between the triangles. [Fig. 7.6] -Maths 9th

Description : If AB = PQ, BC = QR and AC = PR, then write the congruence relation between the triangles. [Fig. 7.6] -Maths 9th

Last Answer : Solution :- △ ABC ≅ △PQR

Let R be a relation defined on the set A of all triangles such that R = {(T1, T2) : T1 is similar to T2}. Then R is -Maths 9th

Description : Let R be a relation defined on the set A of all triangles such that R = {(T1, T2) : T1 is similar to T2}. Then R is -Maths 9th

Last Answer : (d) An equivalence relation.Every triangle is similar to itself, so (T1, T1) ∈ R ⇒ R is reflexive. (T1, T2) ∈ R ⇒ T1 ~ T2 ⇒T2 ~ T1, ⇒ (T2, T1) ∈ R ⇒ R is symmetrictransitive. ∴ R is an equivalence relation.

If vertices of a triangles are (1, k), (4, -3) and (-9, 7) and its area is 15 sq. units then find then the value of k. -Maths 9th

Description : If vertices of a triangles are (1, k), (4, -3) and (-9, 7) and its area is 15 sq. units then find then the value of k. -Maths 9th

Last Answer : hope it helps if the vertices of a triangle are (1,k),(4,−3)(−9,7) area = 15 sq.units. find the value of k. Area of △ 21 [x1 (y2 −y3 )+x2 (y3 −y1 )+x3 (y1 −y2 )]=15 21 [1(−3−7)+ ... k+3)]=15 21 [(−10+28−4k−9k−27)]=15 −10+28−4k−9k−27=30 −10+28−13k−27=30 −13k=30+10+27−28 −13k=39 k=1339 k=−3 thank u

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is -Maths 9th

Description : If one angle of a triangle is equal to the sum of the other two angles, then the triangle is -Maths 9th

Last Answer : (d) Let the angles of a AABC be ∠A, ∠B and ∠C. Given, ∠A = ∠B+∠C …(i) InMBC, ∠A+ ∠B+ ∠C-180° [sum of all angles of a triangle is 180°]…(ii) From Eqs. (i) and (ii), ∠A+∠A = 180° ⇒ 2 ∠A = 180° ⇒ 180° /2 ∠A = 90° Hence, the triangle is a right triangle.

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is -Maths 9th

Description : If one angle of a triangle is equal to the sum of the other two angles, then the triangle is -Maths 9th

Last Answer : (d) Let the angles of a AABC be ∠A, ∠B and ∠C. Given, ∠A = ∠B+∠C …(i) InMBC, ∠A+ ∠B+ ∠C-180° [sum of all angles of a triangle is 180°]…(ii) From Eqs. (i) and (ii), ∠A+∠A = 180° ⇒ 2 ∠A = 180° ⇒ 180° /2 ∠A = 90° Hence, the triangle is a right triangle.

2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal. -Maths 9th

Description : 2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal. -Maths 9th

Last Answer : Consider the following diagram- Here, it is given that AOB = COD i.e. they are equal angles. Now, we will have to prove that the line segments AB and CD are equal i.e. AB = CD. Proof: In triangles AOB ... ) So, by SAS congruency, ΔAOB ΔCOD. ∴ By the rule of CPCT, we have AB = CD. (Hence proved).

5. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. -Maths 9th

Description : 5. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. -Maths 9th

Last Answer : Solution: Given that, Let ABCD be a quadrilateral and its diagonals AC and BD bisect each other at right angle at O. To prove that, The Quadrilateral ABCD is a square. Proof, In ΔAOB and ΔCOD, AO = ... right angle. Thus, from (i), (ii) and (iii) given quadrilateral ABCD is a square. Hence Proved.

If the angles subtended by the chords of a circle at the centre are equal, then chords are equal. -Maths 9th

Description : If the angles subtended by the chords of a circle at the centre are equal, then chords are equal. -Maths 9th

Last Answer : Given : In a circle C(O,r) , ∠AOB = ∠COD To Prove : Chord AB = Chord CD . Proof : In △AOB and △COD AO = CO [radii of same circle] BO = DO [radii of same circle] ∠AOB = ∠COD [given] ⇒ △AOB ≅ △COD [by SAS congruence axiom] ⇒ Chord AB = Chord CD [c.p.c.t]

If the angles subtended by the chords of a circle at the centre are equal, then chords are equal. -Maths 9th

Description : If the angles subtended by the chords of a circle at the centre are equal, then chords are equal. -Maths 9th

Last Answer : Given : In a circle C(O,r) , ∠AOB = ∠COD To Prove : Chord AB = Chord CD . Proof : In △AOB and △COD AO = CO [radii of same circle] BO = DO [radii of same circle] ∠AOB = ∠COD [given] ⇒ △AOB ≅ △COD [by SAS congruence axiom] ⇒ Chord AB = Chord CD [c.p.c.t]

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. -Maths 9th

Description : Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. -Maths 9th

Last Answer : Solution :-

If A, B, C, D are the successive angles of a cyclic quadrilateral, then what is cos A + cos B + cos C + cos D equal to: -Maths 9th

Description : If A, B, C, D are the successive angles of a cyclic quadrilateral, then what is cos A + cos B + cos C + cos D equal to: -Maths 9th

Last Answer : answer:

Let A, B, C be the angles of a plain triangle (A/2) = (1/3 ), tan (B/2) = (2/3). Then tan (C/2) is equal to -Maths 9th

Description : Let A, B, C be the angles of a plain triangle (A/2) = (1/3 ), tan (B/2) = (2/3). Then tan (C/2) is equal to -Maths 9th

Last Answer : answer:

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. -Maths 9th

Description : Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. -Maths 9th

Last Answer : We have a quadrilateral ABCD such that angleO is the mid-point of AC and BD. Also AC ⊥ BD. Now, in ΔAOD and ΔAOB, we have AO = AO [Common] OD = OB [ ... i.e. The rhombus ABCD is having one angle equal to 90°. Thus, ABCD is a square.

Areas of two similar triangles are 36 cm 2 and 100 cm 2 . If the length of a side of thelarger triangle is 20 cm, then the length of the corresponding side of the smaller triangle is: (a) 12cm (b) 13cm (c) 14cm (d) 15cm

Description : Areas of two similar triangles are 36 cm 2 and 100 cm 2 . If the length of a side of thelarger triangle is 20 cm, then the length of the corresponding side of the smaller triangle is: (a) 12cm (b) 13cm (c) 14cm (d) 15cm

Last Answer : (a) 12cm

If the lengths of the sides of a triangle are in the ratio 6:11:15 and it's perimeter is 96cm , then the height corresponding to the longest side is -Maths 9th

Description : If the lengths of the sides of a triangle are in the ratio 6:11:15 and it's perimeter is 96cm , then the height corresponding to the longest side is -Maths 9th

Last Answer : LET EACH SIDE BE X 6X+11X+15X=96 32X=96 X=3 SIDES=6 3=18 11 3=33 15 3=45 AREA OF TRIANGLE BY HERONS FORMULA=S=96/2=48 WHOLE UNDERROOT 48 48-18 48-33 48-45 UNDERROOT=12 4 30 15 3 4 3 15ROOT2 180 ... bh/2 180root2=18 h/2 360root2=18h h=20 root2 But root 2=1.4(approx) h=20 1.4(approx) h=28cm(approx).

If the lengths of the sides of a triangle are in the ratio 6:11:15 and it's perimeter is 96cm , then the height corresponding to the longest side is -Maths 9th

Description : If the lengths of the sides of a triangle are in the ratio 6:11:15 and it's perimeter is 96cm , then the height corresponding to the longest side is -Maths 9th

Last Answer : LET EACH SIDE BE X 6X+11X+15X=96 32X=96 X=3 SIDES=6 3=18 11 3=33 15 3=45 AREA OF TRIANGLE BY HERONS FORMULA=S=96/2=48 WHOLE UNDERROOT 48 48-18 48-33 48-45 UNDERROOT=12 4 30 15 3 4 3 15ROOT2 180 ... bh/2 180root2=18 h/2 360root2=18h h=20 root2 But root 2=1.4(approx) h=20 1.4(approx) h=28cm(approx).

Two points with coordinates (3, 4) and (–5, 4) lie on a line parallel to which axis? Justify your answer. -Maths 9th

Description : Two points with coordinates (3, 4) and (–5, 4) lie on a line parallel to which axis? Justify your answer. -Maths 9th

Last Answer : Solution :- y-coordinate of both the points is 4. So, both points lie on the line y = 4 which is parallel to x-axis.

Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example. -Maths 9th

Description : Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example. -Maths 9th

Last Answer : No, (xy) is necessarily an irrational only when x ≠0. Let x be a non-zero rational and y be an irrational. Then, we have to show that xy be an irrational. If possible, let xy be a rational number. Since ... wrong. Hence, xy is an irrational number. But, when x = 0, then xy = 0, a rational number.

Which of the following expressions are polynomials? Justify your answer, -Maths 9th

Description : Which of the following expressions are polynomials? Justify your answer, -Maths 9th

Last Answer : Following expressions are polynomials .

For what value of x + y in figure will ABC be a line? Justify your answer. -Maths 9th

Description : For what value of x + y in figure will ABC be a line? Justify your answer. -Maths 9th

Last Answer : For ABC to be a line, the sum of the two adjacent angles must be 180° i.e.,x + y = 180°.

Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example. -Maths 9th

Description : Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example. -Maths 9th

Last Answer : No, (xy) is necessarily an irrational only when x ≠0. Let x be a non-zero rational and y be an irrational. Then, we have to show that xy be an irrational. If possible, let xy be a rational number. Since ... wrong. Hence, xy is an irrational number. But, when x = 0, then xy = 0, a rational number.

Which of the following expressions are polynomials? Justify your answer, -Maths 9th

Description : Which of the following expressions are polynomials? Justify your answer, -Maths 9th

Last Answer : Following expressions are polynomials .

For what value of x + y in figure will ABC be a line? Justify your answer. -Maths 9th

Description : For what value of x + y in figure will ABC be a line? Justify your answer. -Maths 9th

Last Answer : For ABC to be a line, the sum of the two adjacent angles must be 180° i.e.,x + y = 180°.

Is every rational number a whole number?Justify your answer. -Maths 9th

Description : Is every rational number a whole number?Justify your answer. -Maths 9th

Last Answer : No, for example 1/5 is a rational number but not a whole number.

1. Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres. -Maths 9th

Description : 1. Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres. -Maths 9th

Last Answer : To recall, a circle is a collection of points whose every point is equidistant from its centre. So, two circles can be congruent only when the distance of every point of both the circles are equal from the centre ... ) So, by SSS congruency, ΔAOB ΔCOD ∴ By CPCT we have, AOB = COD. (Hence proved).

ABC and ADC are two right triangles with common hypotenuse AC. Prove that angle CAD = angle CAB -Maths 9th

Description : ABC and ADC are two right triangles with common hypotenuse AC. Prove that angle CAD = angle CAB -Maths 9th

Last Answer : Given, AC is the common hypotenuse. ∠B = ∠D = 90°. To prove, ∠CAD = ∠CBD Proof: Since, ∠ABC and ∠ADC are 90°. These angles are in the semi circle. Thus, both the triangles are lying in the semi ... D are concyclic. Thus, CD is the chord. ⇒ ∠CAD = ∠CBD (Angles in the same segment of the circle)

Prove that a diagonal of a parallelogram divide it into two congruent triangles. -Maths 9th

Description : Prove that a diagonal of a parallelogram divide it into two congruent triangles. -Maths 9th

Last Answer : Given: A parallelogram ABCD and AC is its diagonal . To prove : △ABC ≅ △CDA Proof : In △ABC and △CDA, we have ∠DAC = ∠BCA [alt. int. angles, since AD | | BC] AC = AC [common side] and ∠BAC = ∠DAC [alt. int. angles, since AB | | DC] ∴ By ASA congruence axiom, we have △ABC ≅ △CDA

On a common hypotenuse AB, two right angled triangles, ACB and ADB are situated on opposite sides. -Maths 9th

Description : On a common hypotenuse AB, two right angled triangles, ACB and ADB are situated on opposite sides. -Maths 9th

Last Answer : According to question ∠BAC = ∠BDC.

ABC and ADC are two right triangles with common hypotenuse AC. Prove that angle CAD = angle CAB -Maths 9th

Description : ABC and ADC are two right triangles with common hypotenuse AC. Prove that angle CAD = angle CAB -Maths 9th

Last Answer : Given, AC is the common hypotenuse. ∠B = ∠D = 90°. To prove, ∠CAD = ∠CBD Proof: Since, ∠ABC and ∠ADC are 90°. These angles are in the semi circle. Thus, both the triangles are lying in the semi ... D are concyclic. Thus, CD is the chord. ⇒ ∠CAD = ∠CBD (Angles in the same segment of the circle)