Use a two-column proof to prove the following theorem:
“The lengths of the corresponding altitudes of similar
Given:
Prove:
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Chapter 5 Solutions
Elementary Geometry for College Students
- a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. Use the fact that the congruent diagonals of a rectangle bisect each other. Be sure to provide a drawing. bUse the relationship from part a to find CM, the length of the median to the hypotenuse of right ABC, in which mC=90, AC = 6, and BC = 8.arrow_forwardA tangent ET is constructed to circle Q from external point E. Which angle and which side of triangle QTE are largest? Which angle and which side are smallest?arrow_forwardGiven the tangents with m3=46, find: a mRST b mRTarrow_forward
- Is it possible to draw a triangle whose sides measure a. 8, 9, and 10? b. 8, 9, and 17? c. 8, 9, and 18?arrow_forwardFor the 30-60-90 triangle shown, suppose that XY=2a. Find: a XZ b YZarrow_forwardWhat relationship, if any, exists between two angles a with equal measures? b that have the same vertex and a common side between them?arrow_forward
- Find the exact perimeter and area of the segment shown, given that mO=600 and OA=12 in.arrow_forwardIn ABC, M is the midpoint of AB and N is the midpoint of AC. If MN= 3x-11 and BC= 4x24, find the value of x._arrow_forwardGiven that mAC:mBC:mAB=4:3:2 in circle O: a Which arc is largest? b Which chord is longest?arrow_forward
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