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For each pair of triangles below, decide whether the triangles are congruent. Justify each conclusion with a flowchart.

  1. 2 triangles oriented in different positions, labeled as follows: Left triangle sides: 6, 8, 9. Right triangle sides: 6, 8, 9.

    Compare the ratios of each of the corresponding sides of the two triangles. What has to be true about these ratios for the triangles to be congruent?

  1. A triangle with a horizontal line drawn internally parallel to the base.

    The two triangles are similar. Justify this by examining the angles of each triangle. Is it possible for these triangles to be congruent?

  1. Two right triangles with bottom sides of 6.

    There is not enough information to determine whether or not the two triangles are similar.

  1. Two triangles. The triangle on the left has a base length of 9. The bottom left vertex angle is 72 degrees. The two other sides have one tick mark. The triangle on the right has a base length of 9 and the angle opposite is 36 degrees. The sides adjacent to the 36 degree angle each have 2 tick marks.

    Both triangles are isosceles. Use this information and the Triangle Sum Theorem to find the values of the unknown angles.