+ Prove Me Wrong C C 4 5 5 10 D A B 3 A B 3 Your friend gives you the right triangle above and to the left and says, "Bisecting an angle is really easy. Take triangle ABC. If I wanted to bisect /CAB, all I need to do is find the midpoint of BC. The ray that goes from A through the midpoint of BC will cut CAB in half, because it cuts the side BC in half." Your friend then sketches the triangle above and to the right. (a) Convince your friend that they are wrong. Use what you know about trigonometry to explain why ZCAD and ZDAB are not congruent. (b) Locate the point E on BC that lies on the angle bisector of /CAB. How far is point E from point B? Show all your work. (c) After you convince your friend that the bisector of ZCAB doesn't go through the midpoint of BC, they say to you, "Now I remember! Every point on an angle bisector is the same distance from the sides of the angle." They draw a line segment from point E that is perpendicular to AC at point F and say, "That means that EB and EF are congruent." Is your friend correct? You can use algebra or trigonometry to confirm or disprove their statement. F C E PERFOR A 3 B 449 Pre-AP Geometry with S

+ Prove Me Wrong C C 4 5 5 10 D A B 3 A B 3 Your friend gives you the right triangle above and to the left and says, "Bisecting an angle is really easy. Take triangle ABC. If I wanted to bisect /CAB, all I need to do is find the midpoint of BC. The ray that goes from A through the midpoint of BC will cut CAB in half, because it cuts the side BC in half." Your friend then sketches the triangle above and to the right. (a) Convince your friend that they are wrong. Use what you know about trigonometry to explain why ZCAD and ZDAB are not congruent. (b) Locate the point E on BC that lies on the angle bisector of /CAB. How far is point E from point B? Show all your work. (c) After you convince your friend that the bisector of ZCAB doesn't go through the midpoint of BC, they say to you, "Now I remember! Every point on an angle bisector is the same distance from the sides of the angle." They draw a line segment from point E that is perpendicular to AC at point F and say, "That means that EB and EF are congruent." Is your friend correct? You can use algebra or trigonometry to confirm or disprove their statement. F C E PERFOR A 3 B 449 Pre-AP Geometry with S

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter6: Equations

Section: Chapter Questions

Problem 3GP

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