Triangles Class 9th Formulas -Maths 9th

Triangles Class 9th Formulas -Maths 9th
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Linear equation in one variable:  Linear equation of the form ax + b = 0, where a, b are real numbers such that a≠ 0. For example, 3x + 5 = 0. The letters used in an equation are called variables or unknowns. In the equation 3x + 5 = 0; x is called the variable of the equation. Linear equation in two variable: An equation of the form ax+ by+ c = 0; where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables. Let us consider the following equations: (i) 3x + y = 7 (ii) 4x – y = 3 (iii) √2x - √3y = 9 (iv) y = 2x + 5 Note : If in the equation ax+ by = c; we have a = 0 and b≠ 0 or b = 0 and a≠ 0 .Then the equation reduces to by = c or ax = c. In both case we get an equation in one variable. So, it is generally assumed that both a and b are non-zero as given in the above definition.  Remember: A linear equation in two variables has infinitely many solutions. • Graph of a linear equation in two variables: The graph of every linear equation in two variables is a striaght line. Algorithm:  To draw the graph of a linear equation in one variable we may follow the following steps: Step I: Obtain the linear equation. Step II : If the equation is of the form ax = b; a ≠ 0 then plot the point (b/a,0) and one more point (b/a, β) where β is any real number on the graph paper. If the equation is of the form ay= b, a ≠ 0 then plot the point (0,b/a) and (α,b/a), where α is any real number on the graph paper. Step III : Join the points plotted in step II to obtain the required line. •The point (a, 0) where the straight line cross x-axis is called its x-intercept point and ‘a’ is called x-intercept. •The point (0, b) where the straight line crosses y-axis is called its y-intercept point and ‘b’ is called y-intercept. • x = 0 is the equation of the y-axis and y = 0 is the equation of the x-axis. •The graph x = a is a straight line parallel to the y-axis. •The graph y = a is a striaght line parallel to the x-axis. •An  equation  of  the  type  y  =  mx represents  a  line  passing through the origin. •Every point on the graph of a linear equation in two variables is  a  solution  of  the  linear  equation.  More over every  solution of the linear equation is a point on the graph of the linear equation.
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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.

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

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

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

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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.

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.

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

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

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.

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 :-

ABC and DBC are two triangles on the same BC such that A and D lie on the opposite sides of BC,AB=AC and DB = DC.Show that AD is the perpendicular bisector of BC. -Maths 9th

Description : ABC and DBC are two triangles on the same BC such that A and D lie on the opposite sides of BC,AB=AC and DB = DC.Show that AD is the perpendicular bisector of BC. -Maths 9th

Last Answer : Solution :-

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Description : Prove that the diagonal divides a parallelogram into two congruent triangles. -Maths 9th

Last Answer : Solution :-

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 :-

Show that the relation ‘≅’ congruence on the set of all triangles in Euclidean plane geometry is an equivalence relation. -Maths 9th

Description : Show that the relation ‘≅’ congruence on the set of all triangles in Euclidean plane geometry is an equivalence relation. -Maths 9th

Last Answer : Reflexive : A ≅ A True Symmetric : if A ≅ B then B ≅ A True Transitive : if A ≅ B and B ≅ C, then A ≅ C True Therefore, the relation ‘≅’ is an equivalence relation.

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.

In the given figure, ABC is a triangle in which CDEFG is a pentagon. Triangles ADE and BFG are equilateral -Maths 9th

Description : In the given figure, ABC is a triangle in which CDEFG is a pentagon. Triangles ADE and BFG are equilateral -Maths 9th

Last Answer : (b) 7√3 cm2.AB = 6 cm, ∠C = 60º (∴ ∠A = ∠B = 60º) ∴ ΔABC is an equilateral triangle Area of ΔABC = \(rac{\sqrt3}{4}\) × (6)2 = 9√3 Area of (ΔADE + ΔBFG) = 2 x \(\bigg(rac{\sqrt3}{4} imes(2)^2\bigg)\) = 2√3 ∴ Area of pentagon = 9√3 - 2√3 = 7√3 cm2.

The hypotenuse of an isosceles right-angled triangle is q. If we describe equilateral triangles (outwards) on all its three sides, -Maths 9th

Description : The hypotenuse of an isosceles right-angled triangle is q. If we describe equilateral triangles (outwards) on all its three sides, -Maths 9th

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Description : Important properties of triangles: -Maths 9th

Last Answer : answer:

Important Theorems on Triangles. -Maths 9th

Description : Important Theorems on Triangles. -Maths 9th

Last Answer : answer:

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Last Answer : answer:

Let ABCD be a cyclic quadrilateral. Show that the incentres of the triangles ABC, BCD, CDA and DAB form a rectangle. -Maths 9th

Description : Let ABCD be a cyclic quadrilateral. Show that the incentres of the triangles ABC, BCD, CDA and DAB form a rectangle. -Maths 9th

Last Answer : answer:

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

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

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What are the 4 congruence for congruent triangles ? -Maths 9th

Description : What are the 4 congruence for congruent triangles ? -Maths 9th

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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

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Description : Simply maths question about rearranging formulas?

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case study questions class 9 maths surface area and volume -Maths 9th

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All the theorems of circles class 9 -Maths 9th

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The class marks of a frequency distribution are 104, 114, 124, 134, 144, 154, 164. -Maths 9th

Description : The class marks of a frequency distribution are 104, 114, 124, 134, 144, 154, 164. -Maths 9th

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