Question is Incomplete,Complete Question is below.
D is a point on the side BC of a triangle ABC such that angle ADC = angle BAC Show that CA square=CB
.CD
Answer:
The Proof is given below.
Step-by-step explanation:
Given:
In ΔABC,
∠ADC = ∠BAC
To Show:
[tex]CA^{2}=CB.CD[/tex]
Proof:
In ΔBAC and ΔADC
∠ADC = ∠BAC ............................Given
∠C = ∠C .....................................Reflexive Property
∴ ΔBAC ~ ΔADC .................... A-A similarity test
If two triangles are similar then their sides are in proportion.
[tex]\dfrac{BA}{AD} =\dfrac{BC}{AC} =\dfrac{AC}{CD}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
[tex]\dfrac{BC}{CA} =\dfrac{CA}{CD}\\\\\therefore CA.CA=CB.CD\\\\\therefore CA^{2}=CB.CD[/tex]..........Proved
