Question

Solve the following problems:

Given: m∠DAB=m∠CBA
m∠CAB=m∠DBA
CA=13 cm
Find: DB

Answer 1

Explanation:

Given : m(∠DAB) = m(∠CBA)

m (CAB) = m(∠DBA)

and CA = 13 cm

To find : measure of DB

In ΔCAB and ΔDAB

m(∠DAB) = m(∠CBA) [given]

m(∠CAB) = m(∠DBA) [given]

and AD is common in both the triangles.

Therefore, ΔCAB and ΔDAB will be congruent. [By ASA property]

Therefore, CA = DB = 13 cm.

Answer 2

DB = 13 cm

Explanation:

ΔCAB ≅ ΔDBA by ASA, so CA ≅ DB by CPCTC.

CA = 13 cm, so DB = 13 cm.