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Home > INT1 > Chapter 8 > Lesson 8.2.1 > Problem 8-102

8-102.

Carefully examine each diagram below and explain why the geometric figure cannot exist. Support your statements with reasons.

  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.

    Read the Math Notes box from Lesson 7.1.6 to review the triangle congruence conjectures.

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

  1. Two line segments intersect, bisecting each other showing 1 tick mark on each side of the first line and 2 tick marks on each side of the second line. A line segment is drawn at both ends creating two triangles. There are two given angles in the left triangle, 40 degrees opposite the side with 1 tick mark, and 50 degrees at the angle where the 2 triangles have a common vertex. The triangle on the right has an 80 degree angle opposite the side with two tick marks.

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

  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 sides are congruent as well.

  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.

    What do you know about isosceles triangles?

  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.