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Harman [31]
2 years ago
8

Given: S is the midpoint of QR, QR¯⊥PS¯ and ∠RSP and ∠QSP are right angles. Prove: PR≅PQ

Mathematics
1 answer:
tigry1 [53]2 years ago
5 0

ΔRSP ≅ ΔQSP by SAS. Therefore, PR ≅ PQ by CPCTC theorem.

<h3>What is the CPCTC Theorem?</h3>

If two triangles are congruent, the CPCTC theorem states that all corresponding parts of the two triangles would also be congruent to each other.

Since S is the midpoint of QR, therefore, RS ≅ QS (one pair of congruent sides)

∠RSP ≅ ∠QSP [right angles] (one pair of congruent included angles)

SP ≅ SP based on the reflexive property (one pair of congruent sides)

Therefore, ΔRSP ≅ ΔQSP by SAS.

Conclusively, PR ≅ PQ by CPCTC theorem.

Learn more about the CPCTC theorem on:

brainly.com/question/6076251

#SPJ1

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The value of the fraction is \rm \sqrt{5} , Option D is the correct answer.

The complete question is

Which choices are equivalent to the quotient below? Check all that apply √75/√15 A. 5 B. √25/√5 C. 15/3 D. √5 E. √3 F. √15/√3

<h3>What is a Fraction ?</h3>

When a number is represented by p/q , where q ≠ 0 is called a fraction.

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\rm \dfrac{\sqrt{75}}{\sqrt {15}}\\\\\\\\dfrac{\sqrt{3*5 *5}}{\sqrt {3*5}}\\\\\\\sqrt{5}\\

Therefore , the value of the fraction is \rm \sqrt{5} , Option D is the correct answer.

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