Description : what- Complete the Angle-Angle-Side Congruence Theorem.If two angles and a non-included side of one triangle are congruent to two angles and a (1) _____ non-included side of another triangle, then the triangles are (2)?
Last Answer : (1) corresponding, (2) congruent
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.
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).
Description : what- Complete the Angle-Side-Angle Congruence Postulate. The same words go in each blank.If _____ and the included side of one triangle are congruent to _____ and the included side of another triangle, then the triangles are congruent?
Last Answer : two angles
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
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
Description : Prove that the diagonal divides a parallelogram into two congruent triangles. -Maths 9th
Last Answer : Solution :-
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).
Description : what- If you are given or can prove that two triangles are congruent, then you may use CPCTC to prove that the angles or sides are?
Last Answer : congruent
Description : There are two congruent triangles each with area 198 cm^2. Triangle DEF is placed over triangle ABC in such a way that the centroid of -Maths 9th
Last Answer : answer:
Description : Prove that median of a triangle divides it into two triangles of equal area. -Maths 9th
Description : Prove that angles opposite to equal sides of a triangle are equal. -Maths 9th
Description : Is this statement true or falseIf two sides and one angle of one triangle are congruent to two sides and one angle of another triangle, then the triangles are congruent by the Side-Angle-Side Postulate?
Description : If the corresponding angles of two triangles are equal, then they are always. State true or false and justify your answer. -Maths 9th
Last Answer : Solution :- False, because two equilateral triangles with sides 3 cm and 6 cm respectively have all angles equal, but the triangles are not congruent.
Description : What are the 4 congruence for congruent triangles ? -Maths 9th
Last Answer : The four congruence are : 1. SSS congruence ( side-side-side). 2. SAS congruence (side-angle-side). 3. ASA congruence (angle-side-angle). 4. RHS congruence (Right-Hypotenuse-Side)
Description : Prove that a triangle must have at least two acute angles. -Maths 9th
Last Answer : Given ΔABC is a triangle. To prove ΔABC must have two acute angles Proof Let us consider the following cases Case I When two angles are 90°. Suppose two angles are ∠B = 90° and ∠C = 90°
Description : Prove that a triangle must have atleast two acute angles. -Maths 9th
Description : ABC is an isosceles triangle in which AB=AC.AD bisects exterior angles PAC and CD parallel AB.Prove that-i)angle DAC=angle BAC ii)∆BCD is a parallelogram -Maths 9th
Last Answer : AB =AC(given) Angle ABC =angle ACB (angle opposite to equal sides) Angle PAC=Angle ABC +angle ACB (Exterior angle property) Angle PAC =2 angle ACB - - - - - - (1) AD BISECTS ANGLE PAC. ANGLE ... AND AC IS TRANSVERSAL BC||AD BA||CD (GIVEN ) THEREFORE ABCD IS A PARALLEGRAM. HENCE PROVED........
Description : Bisectors of angles A, B and C of a triangle ABC intersects its circumcircle at D, E and F respectively. Prove that angles of triangle DEF are 90° - A/2, 90° - B/2 and 90° - C/2. -Maths 9th
Last Answer : We have ∠BED = ∠BAD (Angles in the same segment) ⇒ ∠BED = 1/2∠A ...(i) Also, ∠BEF = ∠BCF (Angles in the same segment) ⇒ ∠BEF = 1/2∠C ...(ii) From (i) and (ii) ∠BED + ∠BEF = 1/2∠A + 1/2∠C ∠DEF ... ∠A + ∠C) ⇒ ∠DEF = 1/2(180° - ∠B) (Since, ∠A + ∠B + ∠C = 180°) ⇒ ∠DEF = 90° - 1/2∠B
Description : State and prove-line joining the midpoint of any two sides of a triangle is parallel to throw side and is equal to 1/2 of it -Maths 9th
Last Answer : Here, In △△ ABC, D and E are the midpoints of sides AB and AC respectively. D and E are joined. Given: AD = DB and AE = EC. To Prove: DE ∥∥ BC and DE = 1212 BC. Construction: Extend line segment DE to ... we have DF ∥∥ BC and DF = BC DE ∥∥ BC and DE = 1212BC (DE = EF by construction) Hence proved.
Description : Two congruent circles intersect each other at point A and B.Through A any line segment PAQ is drawn so that P,Q lie on the two circles.Prove that BP = BQ. -Maths 9th
Last Answer : Solution :- Let, O and O' be the centres of two congruent circles. As, AB is the common chord of these circles. ∴ ACB = ADB As congruent arcs subtent equal angles at the centre. ∠AOB = ∠AO'B ⇒ 1/2∠AOB = 1/2∠AO'B ⇒ ∠BPA = ∠BQA ⇒ BP = BQ (Sides opposite to equal angles)
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.
Description : what- Fill in the blanks to the Hypotenuse- Leg Congruence Theorem.If the hypotenuse and leg of one right triangle are _____ to the _____ of another right triangle, then the triangles are congruent?
Last Answer : congruent; hypotenuse and a leg
Description : Which arrangement cannot be used to prove two triangles congruent?
Last Answer : SSA
Description : Prove that in a triangle,other than an euilateral triangle, angle opposite the longest side is greater than 2/3 of a right angle. -Maths 9th
Description : Is this statement true or falseThere is enough information to prove the triangles congruent using HL?
Last Answer : 1
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
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
Description : Is a shape split into two congruent triangles with different base angles a parallelogram?
Last Answer : Yes, a parallelogram or a rhombus would fit the givendescription.
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)
Description : Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side -Maths 9th
Description : If circles are drawn taking two sides of a triangle as diameter, prove that the point of intersection of these circles lie on the third side. -Maths 9th
Last Answer : Solution :- Given: Two circles are drawn on sides AB and AC of a △ABC as diameters. The circles intersects at D. To prove: D lies on BC Construction: Join A and D Proof: ∠ADB = 90° (Angle in the semi-circle ... + 90° => ∠ADB + ∠ADC = 180° => BDC is a straight line. Hence, D lies On third side BC.
Description : If two lines intersect prove that the vertically opposite angles are equal. -Maths 9th
Last Answer : Given Two lines AB and CD intersect at point O.
Description : In a right angle triangle, prove that the hypotenuse is the longest side. -Maths 9th
Last Answer : The sum of angles of a triangle is180° If one aangke is of 90° then the sum of two angles is 90° It means that the angle forming 90° is biggest angle We know , Angle opposite to the longest side is largest. It means hypotenuse is the biggest side of right angled triangle
Description : Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side, if intersect they will intersect on the circumcircle of the triangle. -Maths 9th
Last Answer : According to question prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side,
Description : If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles. -Maths 9th
Description : In the given figure, equal chords AB and CD of a circle with centre O cut at right angles at E. If M and N are the mid-points of AB and CD respectively, prove that OMEN is a square. -Maths 9th
Last Answer : Join OE. In ΔOME and ΔONE, OM =ON [equal chords are equidistant from the centre] ∠OME = ∠ONE = 90° OE =OE [common sides] ∠OME ≅ ∠ONE [by SAS congruency] ⇒ ME = NE [by CPCT] In quadrilateral OMEN, ... =ON , ME = NE and ∠OME = ∠ONE = ∠MEN = ∠MON = 90° Hence, OMEN is a square. Hence proved.
Description : The angles of a triangle are in the ratio 8 : 3 : 1. What is the ratio of the longest side of the triangle to the next longest side? -Maths 9th
Description : If two chords AB and CD of a circle AYDZBWCX intersect at right angles, then prove that arc CXA + arc DZB = arc AYD + arc BWC = semi-circle. -Maths 9th
Last Answer : Given In a circle AYDZBWCX, two chords AB and CD intersect at right angles. To prove arc CXA + arc DZB = arc AYD + arc BWC = Semi-circle. Construction Draw a diameter EF parallel to CD having centre M. Proof ... (i) arc ECXA = arc EWB [symmetrical about diameter of a circle] arc AF = arc BF (ii)