Question

BCD is a triangle.

ABD is a straight line.
Angle ABC = 124°
Angle BDC = 62°
1249
B
A
Determine what type of triangle BCD is.
Give a reason for each stage of your working.
62
D


SHOW WORKING

Answer 1

Δ BCD is an isosceles triangle

Explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ABC is an exterior angle of the triangle , then

∠ BDC + ∠ BCD = ∠ ABC

62° + ∠ BCD = 124° ( subtract 62° from both sides )

∠ BCD = 62°

then ∠ BDC = ∠ BCD = 62°

thus the 2 base angles of the triangle are congruent

then triangle BCD is isosceles with BC = BD