Simple Proofs for Congruence in Triangles

Lesson

Practice

Interactive practice questions

Which pairs of triangles are congruent?

Give the reason for the congruence.

AAS: Two equal angles and one included side

RHS: Two right-angled triangles with equal hypotenuses and one equal side.

SSS: Three equal sides

SAS: Two equal sides and one included angle

Easy

< 1min

Write a mathematical expression stating that the two triangles are congruent, naming the vertices in corresponding order.

Easy

1min

Consider the two triangles below:

Easy

< 1min

An isosceles triangle is cut along its perpendicular height.

Easy

< 1min

Outcomes

9.G.T.1

Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence). Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

9.G.T.2

Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. The angles opposite to equal sides of a triangle are equal. The angles opposite to equal sides of a triangle are equal. Triangle inequalities and relation between ‘angle and facing side’; inequalities in a triangle.

9.G.Q.1

The diagonal divides a parallelogram into two congruent triangles. In a parallelogram opposite sides are equal and conversely. In a parallelogram opposite angles are equal and conversely. A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal. In a parallelogram, the diagonals bisect each other and conversely.

Simple Proofs for Congruence in Triangles

Interactive practice questions

Outcomes

9.G.T.1

9.G.T.2

9.G.Q.1

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