Expert answers to "To explain: The way to know that each..."

waigaK

Answered question

2021-07-31

To explain: The way to know that each pair of triangle is congruent.
Given:
The given figure is as follows.

Aubree Mcintyre

Skilled2021-08-01Added 73 answers

Calculation:
From the figure, it can be observed that

\overset{―}{S T} \tilde{=} \overset{―}{T Q}, and \overset{―}{R T} \tilde{=} \overset{―}{P T}

.
By the Vertical Angles Theorem,

∠ P T Q \tilde{=} ∠ R T S

.
By SAS Congruence Theorem,

△ P T Q \tilde{=} △ R T S

.
In the similar reasoning as above

△ P T S \tilde{=} △ R T Q

.
Thus, the congruence triangle are

△ P T Q \tilde{=} △ R T S, and △ P T S \tilde{=} △ R T Q

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