Question

Given:
HB PERP. AD
EC PERP AD
AB CONG CD
FA CONG FD
Prove:
ANGLE AHB CONG. ANGLE DEC

Answer 1

is ADF a triangle, do lines AF and DF join at the top?

Answer 2

YES they do . sorry bad diagram

Answer 3

so
in triangle AHB and triangle CED
bcoz
FA= FD ==>
<A = <D (angles opposite to equal sides are equal)
<B = <C (each equa; 90 HB PERP. AD EC PERP AD )

Answer 4

so remaing <H and <E are also equal

Answer 5

Since that is the case, angles BAH and CDE are equal as they are opposite equal sides of a triangle. matricked has already explained also.

Answer 6

Alternatively
in triangle AHB and triangle CED

<B = <C (each equa; 90 HB PERP. AD EC PERP AD )
<A = <D (as shown earlier)
AB = CD
so triangle AHB and triangle CED are congruent
hence
<AHB =< DEC (corresponding parts of congruent triangles)

Answer 7

by what theorem / postulate is <H CONG<E

Answer 8

<H = 180 - <A - <B [<A = <D and <B = <C ]
= 180 -<D-<C
=<E

Answer 9

The sum of the interior angles equals 180 degrees in a triangle. You have two angles of one triangle equal to the corresponding angles of another triangle, There sum would be equal thus the sum subtracted from 180 degrees would reveal the third angle would also be equal/

Answer 10

thank you so much @matricked and @radar I think I got it :)

Answer 11

yw

Answer 12

You're welcome, equals subtracted from equal, the remainder will also be equal; Good luck with your studies.