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Identify if each pair of triangles below is congruent or not. Remember that the diagrams may not be drawn to scale. Justify your conclusion. Redraw and label the diagrams as needed.  

Read the Math Notes box on triangle congruence conditions.

  1. Two triangles sharing one side. One set of adjacent sides where the sides are in opposite triangles have 1 tick mark.  The other set has 2 tick marks.

    What do the tick marks on the sides mean? Do they help prove the triangles are congruent?

    How many sides are congruent in the two triangles is that enough to prove the triangles congruent?

  1. Two triangles with intersecting lines between them are connected at the point of intersection. One of the intersecting lines has a length of 10, 5 on either side of the point of intersection. The other intersecting line has a length of 4 on one side of the intersection. For the triangle that does not have 2 sides labeled, it has a side, 4, which is opposite the angle at the point of intersection.

    How could you prove the triangles are congruent? Is there enough information? Are the parts in the correct order?

  1. Two triangles, the first rotated 180 degrees and translated 3 to the right. Both triangles have one angle marked with one tick mark and a second angle marked with two tick marks.

    How do the tick marks on the angles provide enough information to prove they are congruent?

    Are there any congruent sides in this figure?

  1. A triangle with a line drawn from the top vertex to the base. The left angle the line creates with the base is 90 degrees. The triangle's long sides are both marked with one tick mark.

    What type of triangle is this? What information do you know about the triangle by knowing its name?

    What relationship could be used to prove they are congruent?