Question

prove that in a right angle triangle if altitude is drawn to the hypotenuse then two triangles formed will be similar to original triangle and to each other ​

Answer 1

Step-by-step explanation:

correct answer for your question

Answer 2

Given:

The altitude is drawn to the hypotenuse.

To Find:

To prove that in a right angles triangle two triangles formed will be similar to the original triangle and each other.

Solution:

It is given that altitude is drawn to the hypotenuse in a right-angled triangle.

As we know, If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and each other.

Now, draw a line perpendicular to BD and AC.

Then, in ΔABD and ΔABC

ΔADB ≅ ΔABC [ both are congruent because they are 90°]

∠A ≅ ∠A [common angles of the triangle]

Now, by AA similarity criteria  

ΔADB ~ΔABC.(i)

Then, in ΔBDC and ΔABC

ΔBDC ≅ ΔABC  

BDC ≅ ABC [both 90°]

∠C ≅ ∠C [common angles of a triangle]

Now, again by AA similarity criteria

ADC is similar to ABC ..(ii)

Using (i) and (ii) we get

ΔADB is similar to triangle ΔBDC.

∴ΔADB ~ ΔBDC