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Chapter 5: Q24 (page 188)

RA炉is an altitude of 螖SAT . P and Q are midpoints of SA炉and TA炉. SR=9, RT=16, QT=10, and PR=7.5.

Find RQ.

Short Answer

Expert verified

RQ=10

Step by step solution

01

Step 1. Consider the diagram.

Here, RA炉is an altitude of 螖SAT. P and Q are midpoints of SA炉and TA炉. SR=9, RT=16, QT=10, and PR=7.5 .

02

Step 2. Show the calculation.

Consider the triangle 螖SAT.

It is given that RA炉is an altitude of 螖SAT.

So, it can be said that the triangle 螖ART is a right triangle.

Now, TA炉is the hypotenuse of the right triangle 螖ART and Q is its midpoint.

So, by theorem 5-15, the midpoint Q of the hypotenuse TA炉of a right triangle 螖ARTis equidistant from the three vertices.

03

Step 3. State the conclusion.

Therefore,RQ=TQ=10

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In Exercises 5-10 quad. PQRS is a parallelogram. Find the values of a, b, x and y.

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