### Congruence of Triangles - Worksheets

CBSE Worksheet-1

CLASS –VII Mathematics (Congruence of Triangles)

Choose correct option in questions 1 to 4.

- ΔABC and ΔPQR are congruent under the correspondence ABC ↔ RQP

Write the parts of ΔABC that correspond to RQ.

a. AB

b. BC

c. AC

d. none of these - Which angle is included between the sides DE and EF of ΔDEF?

a. ∠D

b. ∠E

c. ∠F

d. none of these - By applying SAS congruence rule, you want to establish that ΔPQR ≅ ΔFED. It is given that PQ = FE and RP = DF. What additional information is needed to establish the congruence?

a. ∠P = ∠D

b. ∠Q = ∠D

c. ∠P = ∠F

d. ∠R = ∠F - Which congruence criterion do you use in the following?

Given: AC = DF, AB = DE, BC = EF. So, ΔABC ≅ ΔDEF

a. ASA rule

b. SAS rule

c. RHS rule

d. SSS rule

Fill in the blanks:

- If two-line segments have the ____________ length, they are congruent.
- If two triangles are congruent, then their ____________ parts (i.e., angles and sides) that match one another are equal.
- In an isosceles triangle base angles opposite to the equal sides are __________.
- The side opposite to the right angle is called the _________ of the right-angled triangle.
- In triangles ABC and PQR, AB = 3.5 cm, BC = 7.1 cm, AC = 5 cm, PQ = 7.1 cm, QR = 5 cm and PR = 3.5 cm. Examine whether the two triangles are congruent or not. If yes, write the congruence relation in symbolic form.
- In the following figure, AB and CD bisect each other at O. State the three pairs of equal parts in two triangles AOC and BOD.

CBSE Worksheet-1

CLASS –VII Mathematics (Congruence of Triangles)

Answer key

- c

Explanation: Since ABC ↔RQP is the correspondence of triangles ΔABC and ΔPQR,

We can say that AB ↔RQ - b

Explanation: The vertex common to the sides DE and EF is E. Hence the included angle is ∠E. - c

Explanation: By SAS congruence rule, two triangles are congruent if two sides and the angle included between them of a triangle are equal to two corresponding sides and the angle included between them of another triangle.

Here Given that PQ = FE and RP = DF, the angle included these two sides are ∠P and ∠F.

Hence ∠P = ∠F. - d

Explanation: Since the three sides of the one triangle is equal to the corresponding sides of the other triangle, as per the SSS congruence criterion is used here. - equal
- corresponding
- equal
- hypotenuse
- Yes ΔABC ≅ ΔRPQ by SSS Congruency

Explanation: The sides of the triangle ABC are AB, BC, AC and that of triangle PQR are PQ, QR, PR

Given that, AB = PR = RP = 3.5cm

BC = PQ = 7.1cm

AC = RQ = 5cm

Hence by SSS congruency rule, since the three sides are equal the triangles ABC and RPQ are congruent

ΔABC ≅ ΔRPQ. - AO = BO, OC = OD and ∠AOC =∠BOD (vertically opposite angle)

Explanation:

Since AB and CD bisect each other at O, AO = BO and OC = OD. Since ∠ AOC and ∠ BOD are vertically opposite angles formed by the intersection of the line segments AB and CD,

∠AOC = ∠BOD

Hence equal parts of the two triangles AOC and BOD are

AO = BO, OC = OD and ∠AOC =∠BOD.