Question

In the given figure, PQ || RS and PQ = RS. Prove that ΔPUQ = ΔSUR

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Answer 1

Answer:

THE ANSWER IS SAS

Step-by-step explanation:

Answer 2

Answer:

$\triangle S U R$

Explanation:

Step : 1 In $\triangle P U Q$ and $\triangle S U R$

$\begin{aligned}& \mathrm{PQ}=\mathrm{SR}=4 \mathrm{~cm} \\& \angle \mathrm{UPQ}=\angle \mathrm{SR} \text { (Alternate interior angles) } \\& \angle P Q U=\angle S R U \text { (Alternate interior angles) } \\& \triangle P U Q=\triangle S U R \text { (By ASA rule) }\end{aligned}$

Step : 2When two lines are divided by a transversal, a third line, the phrase alternating internal angles is frequently used. The pairs of alternate interior angles are congruent, according to the Alternate Interior Angles Theorem, if k and l are parallel. That is, $\angle 2 \cong \angle 8 \text { and } \angle 3 \cong \angle 5$

Step : 3alternative angle, noun: one of a pair of angles between the two intersected lines and on opposing sides of a line that connects two other lines. One of a pair of angles outside the two crossed lines and on the opposing sides of a line that crosses two other lines is known as an alternative interior angle.

Step : 4The alternative interior angles theorem states that if two parallel lines are intersected by a transversal, the alternate interior angles are identical in magnitude. With the aid of this theorem, we may determine the measure of an alternative interior angle if we are aware of the measurement of the corresponding alternate interior angle.

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