The diagram shows a right angked triangle where angle BAC=90 . A perpendicular is drawn from A to meet the hypothenus BC at D . Prove that triangles ABC , DBA , and DAC are similar .

Is angle BAD = angle DAC ??

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- Oct 15th 2009, 11:07 PMthereddevilsright angled triangle
The diagram shows a right angked triangle where angle BAC=90 . A perpendicular is drawn from A to meet the hypothenus BC at D . Prove that triangles ABC , DBA , and DAC are similar .

Is angle BAD = angle DAC ?? - Oct 16th 2009, 12:59 AMred_dog
No.

In the triangle ADB:

In the triangle ABC:

Then

In the same way, - Oct 16th 2009, 07:56 AMSoroban
Hello, thereddevils!

Quote:

The diagram shows a right-angled triangle where angle BAC=90°.

A perpendicular is drawn from A to meet the hypothenus BC at D.

Prove that triangles ABC, ADB, and ADC are similar .Code:`A`

*

*|4 *

*3| *

* | *

* | *

* 1 | 2 *

B * * * * * * * * * C

D

In right triangle are complementary: .

In right triangle are complementary: .

. . Hence: .

So and have equal angles:

. .

Therefore: .

Similarly, prove that