CPM Homework Help : CCG Problem 7-78

Tromika wants to find the area of the isosceles triangle below.

Triangle A, B, C with side B, C, 8. Sides A, B, and A, C, have 1 tick mark each. Angle A measures 36 degrees.

She decided to start by drawing a height from vertex $A$ to side $\overline{BC}$ as shown at right. Will the two smaller triangles be congruent? In other words, is $ΔABD≅ΔACD$ ? Why or why not?

Hint (a):
Look at the two triangles that are created. They share a side, and the ticks marks mean the sides are equal. How could they be congruent?
Answer (a):
Yes, they are congruent by $HL≅$ .

Triangle, A B C, dashed segment from vertex A, perpendicular to side, B C, at point, D, Side, B C, labeled 8, Angle, B A C, labeled 36 degrees, Sides, A B, & A C, each have 1 tick mark.

What is $m∠DAB$ ? $BD$ ?
Hint (b):
If the segment (height) bisects both $∠BAC$ and segment $BC$ , how can you calculate the measure of half of each?
Answer (b):
$m∠DAB=18°$
$BD=4$
Find $AD$ . Show how you got your answer.
Hint (c):
Which trig ratio can you use to determine this length?
Find the area of $ΔABC$ .
Hint (d):
How do you find the area of a triangle? Do you have enough information to calculate the area?