If ∆ABC and ∆DBC are on the same base BC, AB = DC and AC = DB (Fig. 6.21), then which of the following gives a congruence relationship?
(a) ∆ ABC ≅ ∆ DBC
(b) ∆ ABC ≅ ∆CBD
(c) ∆ ABC ≅ ∆ DCB
(d) ∆ ABC ≅ ∆BCD

Solution:

Given, ∆ABC and ∆DBC are on the same base BC.

Also, AB = DC and AC = DB

We have to find the type of congruence criteria.

Side-Side-Side congruence rule states that if three sides of one triangle are equal to three corresponding sides of another triangle, then the triangles are congruent.

By SSS rule,

Given, AB = DC

AC = DB

Common side = BC

So, triangle ABC is congruent to DCB.

Therefore, ∆ ABC ≅ ∆ DCB

✦ Try This: In △PQR, if ∠P = 80° and ∠Q = 88°, find ∠R (in degrees)

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 49

If ∆ABC and ∆DBC are on the same base BC, AB = DC and AC = DB (Fig. 6.21), then which of the following gives a congruence relationship? (a) ∆ ABC ≅ ∆ DBC, (b) ∆ ABC ≅ ∆CBD, (c) ∆ ABC ≅ ∆ DCB, (d) ∆ ABC ≅ ∆BCD

Summary:

If ∆ABC and ∆DBC are on the same base BC, AB = DC and AC = DB (Fig. 6.21), then ∆ ABC ≅ ∆ DCB gives a congruence relationship.

☛ Related Questions:

• The ________ triangle always has altitude outside itself. Fill in the blanks to make the statement t . . . .
• The sum of an exterior angle of a triangle and its adjacent angle is always ______. Fill in the blan . . . .
• The longest side of a right angled triangle is called its _______. Fill in the blanks to make the st . . . .