Given:
AC – AR
<1 = <2
Prove:
<3 =<4

Proved: <3 =<4

Step-by-step explanation:

Alternate angles are equal

<1 = <4

<2 = <3

AC ≅ AR (Given)

Where ≅ means congruent to

When two straight lines intersect, the Vertical angles have opposite sides that are equal.

<CAR ≅ <TAD

<CAT ≅ <RAD

From the above

∆CAR is congruent to ∆TAD

This is a side angle side theorem

∆CAT is congruent to ∆RAD

This is a side angle side theorem

The side angle side theorem shows that two sides and an included angle of one triangle are equal to two sides and an included angle of another triangle.

Since corresponding parts of congruent angles are equal, <3 is congruent to <4.

<3 ≅ <4

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