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3 years ago

Given: <SPT = <RQT, ST = RT Prove: PR = QS

Mathematics

1 answer:

andrey2020 [161]3 years ago

7 0

Answer:

See explanation

Step-by-step explanation:

Consider triangles PTS and QTR. In these triangles,

$ST=RT$ - given;
$\angle SPT=\angle RQT$ - given;
$\angle STP=\angle RTQ$ - as vertical angles when lines PR and SQ intersect.

Thus, $\triangle PTS\cong \triangle QTR$ by AAS postulate.

Congruent triangles have congruent corresponding sides, so

$PT=QT$

Consider segments PR and QS:

$PR=PT+TR\ [\text{Segment addition postulate}]\\ \\QS=QT+TS\ [\text{Segment addition postulate}]\\ \\PT=QT\ [\text{Proven}]\\ \\ST=RT\ [\text{Given}]$

So,

$PR=SQ\ [\text{Substitution property}]$

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3 years ago

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$\huge \boxed{\mathbb{QUESTION} \downarrow}$

$- 2 ( 2 x + 3 ) \leq 26.$

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$- 2 ( 2 x + 3 ) \leq 26$

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Given: <SPT = <RQT, ST = RT Prove: PR = QS​

Given: <SPT = <RQT, ST = RT Prove: PR = QS