Advertisement Remove all ads

Use the Information Given in the Following Figure to Prove Triangles Abd and Cbd Are Congruent. Also, Find the Values of X and Y. - Mathematics

Sum

Use the information given in the following figure to prove triangles ABD and CBD are congruent. Also, find the values of x and y.

Advertisement Remove all ads

Solution

Given: In the figure AB = BC, AD = DC

∠ABD = 50, ∠ADB = y − 7°

∠CBD = x + 5°, ∠CDB = 38°

To find: The value of x and y

In Δ ABD and Δ CBD

BD = BD ........(common)

AB = BC ........(given)

AD = CD ...........(given)

∴ Δ ABD ≅ Δ CBD .........(SSS axiom)

∴ ∠ABD = ∠CBD 

⇒ 50 = x + 50° 

⇒ x = 50° − 5° = 45°

and ∠ADB = ∠CDB

⇒ y − 7° = 38°

⇒ y = 38° + 7° = 45°

Hence x = 45°, y = 45°

Concept: Extend Congruence to Simple Geometrical Shapes E.G. Triangles, Circles.
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Selina Concise Mathematics Class 7 ICSE
Chapter 19 Congruency: Congruent Triangles
Exercise 19 | Q 14
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×