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, 7e
- 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_forwardCircles O, P, and Q are tangent as shown at points X, Y, and Z. Being as specific as possible, explain what type of triangle PQO is if: a OX=2,PY=3,QZ=1 b OX=2,PY=3,QZ=2arrow_forwardDetermine the type of triangle represented if the lengths of its sides are: a a=1.5, b= 2 and c = 2.5 b a= 20, b= 21 and c = 29 c a=10, b= 12, and c =16 d a= 5, b= 7 and c = 9arrow_forward
- A 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_forwardIs 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_forward
- For 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_forwardFor the 30-60-90 triangle shown, suppose that XZ=a. Find: a YZ b XYarrow_forward
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