5. The triangle ABC has the following property. The distance from vertex C to the midpoint of side AB is half the distance from A to B. (a) Show that the measure of angle BCA equals the sum of the measures of angles ABC and CAB. (b) Show that the measure of angle BCA is 90°.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter4: Quadrilaterals
Section4.3: The Rectangle, Square, And Rhombus
Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...
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5. The triangle ABC has the following property. The distance from
vertex C to the midpoint of side AB is half the distance from A to B.
(a) Show that the measure of angle BCA equals the sum of the measures
of angles ABC and CAB.
(b) Show that the measure of angle BCA is 90°.
6. What is the sum of the angles a, b, c, d, e, and f (in degrees)? Justify your answer.
7. Use only straightedge and compass to construct an angle of 135°. Describe the procedure you
followed.
Transcribed Image Text:5. The triangle ABC has the following property. The distance from vertex C to the midpoint of side AB is half the distance from A to B. (a) Show that the measure of angle BCA equals the sum of the measures of angles ABC and CAB. (b) Show that the measure of angle BCA is 90°. 6. What is the sum of the angles a, b, c, d, e, and f (in degrees)? Justify your answer. 7. Use only straightedge and compass to construct an angle of 135°. Describe the procedure you followed.
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