Topics
Geometry
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India
Class IX

Proofs Using Congruent Triangles

Lesson

Interactive practice questions

In the diagram, $AB=CB$AB=CB and $D$D is the midpoint of side $AC$AC.

Without using the properties of an isosceles triangle show that $\angle BAD=\angle BCD$∠BAD=∠BCD.

In $\triangle BAD$△BAD and $\triangle BCD$△BCD we have:

Easy
4min

In the diagram , $AE$AE and $BD$BD bisect one another.

Prove that $AB\parallel ED$AB∥ED.

Easy
5min

In the following diagram, $X$X is the centre of a circle.

By proving $\triangle XBC$△XBC is congruent to $\triangle XGF$△XGF, show that $AD\parallel EH$AD∥EH.

Easy
5min

$ABCD$ABCD is a parallelogram with $AE=FC$AE=FC. Prove that $DE$DE=$FB$FB.

Medium
5min
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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.

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