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Home > CCG > Chapter 7 > Lesson 7.2.6 > Problem 7-110

7-110.

Carefully examine each diagram below and explain why the geometric figure cannot exist. Support your statements with reasons. If a line looks straight, assume that it is.  

Review the triangle congruence conjectures.

  1. Two triangles. The triangle on the left has side lengths 4, 5, and 7, with one angle of 80 degrees between sides 7 and 4. The triangle on the right has side lengths 4, 5, and 7, with one angle of 50 degrees between sides 4 and 7.

  1. Two line segments intersect, with segments enclosing the left & right ends to create 2 triangles, left triangle labels as follows: right top side, 1 tick mark, bottom right side, 2 tick marks, bottom left angle, 40 degrees, angle opposite left side, 50 degrees, right triangle, top left side, 2 tick marks, bottom left side, 1 tick mark, angle opposite top left side, 80 degrees.

  1. A triangle with a left side 12, and right side 10. Two internal triangles are created, by a line segment drawn from the upper vertex, perpendicular to the base bisecting the bottom base.

  • The triangles should be congruent by , but and in congruent triangles all angles are equal as well.

  • The triangles should be congruent by , but and and in congruent triangles all angles are equal as well.

  • The triangles should be congruent by  , but and in congruent triangles all sides are congruent as well.

What do you know about isosceles triangles?

  1. Triangle labeled as follows: bottom left angle, 50 degrees, bottom right angle, 60 degrees, left side and right side, each have one tick mark.

  1. Triangle, with line segment from upper vertex, to the center of the bottom side, labeled as follows: bottom left angle, 50 degrees, bottom right angle, 60 degrees, left side and right side, each have one tick mark.

  1. Triangle labeled as follows: left side, 15, right side, 13, left base angle, one tick mark. A second triangle, whose top side, is the same as the bottom side of the first triangle, labeled as follows: left side, 15, right side, 14, left top angle, one tick mark.

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