Question

In the figure below, there are three right trangles. Complete the following.

A
C
D
B
(a) Write a similiarity statement relating the three right triangles.
ACDA~A~A
(b) Complete each proportion.
BD
BC
BC
DA
DC
=
0
BD
X
5

Answer 1

Part (a)

Let one of the angles be
`\theta`. After solving for all of the other angles using the triangle sum theorem, we see that
`\triangle CDA \sim \triangle BDC \sim \triangle BCA`.

Part (b)

`(BD)/(BC)=(BC)/(CA), (DA)/(DC)=(DC)/(DB)`