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CR and DS are perpendiculars dropped from AB to PQ , and AB is perpendicular to CR and DS . If CR = DS, which statement must be true?

User Loic
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2 Answers

3 votes

Final answer:

Since CR and DS are perpendicular to AB and equal in length, they must also be perpendicular to each other, forming a 90° angle, which confirms statement (b) as true.

Step-by-step explanation:

The student's question involves understanding geometric properties specifically related to perpendicular lines. If CR and DS are both perpendicular to AB, and CR = DS, then CR and DS are also perpendicular to each other and form a right angle (90° angle) between each other, which means that statement (b) 'They are perpendicular, forming a 90° angle between each other.' must be true.

This follows from the properties of a rectangle or a right angled triangle, where the sides meeting at a right angle are mutually perpendicular. Given that AB is also perpendicular to both CR and DS, we can infer that AB, CR, and DS form three mutually perpendicular lines, creating a three-dimensional rectangular corner, thus confirming our selection of statement (b).

User Real Noob
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7.5k points
4 votes

Answer:

m∠RCD = m∠ACD ÷ 2

Step-by-step explanation:

User Gricel
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7.6k points