Triangle Congruence Rules and Practice Worksheet Solutions

Published on October 2, 2026

Geometry

Step-by-step solutions for Grade 7 geometry worksheet on triangle congruence rules including SSS and SAS postulates, corresponding parts, and proofs.

Question

Solve it

Answer

Here are the step-by-step solutions for the worksheet:

1. Fill in the blanks

a) According to the SSS congruence rule, if the three sides of one triangle are equal to the corresponding sides of another triangle, then the triangles are congruent.
b) If

by SSS, then

.
c) If

and

, then

is congruent to

.
d) If all three sides of two triangles are equal, their corresponding angles will also be equal.
e) Full form of CPCT is Corresponding Parts of Congruent Triangles.
f) If

by SSS, then

because corresponding parts of congruent triangles are equal.
g) SAS stands for Side – Angle – Side.
h) According to the SAS rule, if two sides and the included angle of one triangle are equal to the corresponding parts of another triangle, then the triangles are congruent.

2. Congruence of

Other ways of expressing congruence:

Corresponding Vertices:

Corresponding Sides:

Corresponding Angles:

3. Identify triangles congruent to

has sides

, and

(i) : Sides are . (Congruent)
(ii) : Sides are . (Congruent)
(iii) : Sides are . (Congruent)
(iv) : Sides are . (Not congruent)

Answer: Triangles (i), (ii), and (iii) are congruent to

4. Congruence of and

Given:
Sides of

Sides of

Since all three sides of

are equal to the three corresponding sides of

, the triangles are congruent by the SSS (Side-Side-Side) congruence rule.

5. Prove Congruence

a) and (or and ):
Looking at the figure, we have two triangles sharing a common side

.
In

and

(considering the two halves of the quadrilateral):

(Given)
(Common side)
(Wait, looking at labels: and )
Actually, the figure shows a quadrilateral . Let’s look at and :
(Wait, labels are and - assuming and are the bottom vertices).
The two triangles have sides .
Rule: by SSS rule.