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IM Geo.2.11 Lesson: Side-Side-Angle (Sometimes) Congruence

What do you notice? What do you wonder?

In triangles  and :

  • Angle  is congruent to angle .
  • Segment  is congruent to segment .
  • Segment  is congruent to segment .

Use the applet below to make a triangle using the given angle and side lengths so that the given angle is not between the 2 given sides. Try to make your triangle different from the triangles created by the other people in your group.
  • Angle: 
  • Side length: 6 cm
  • Side length: 8 cm

Your teacher will assign you some sets of information.

  • For each set of information, use the applet below to make a triangle using that information.
  • If you think you can make more than one triangle, make more than one triangle.
  • If you think you can’t make any triangle, note that.

When you are confident they are accurate, create a visual display.

Triangle ABC is shown. Use your straightedge and compass to construct a new point D on line AC so that the length of segment BD is the same as the length of segment BC.

Now use the straightedge and compass to construct the midpoint of . Label that midpoint . Explain why triangle  is a right triangle.

Explain why knowing the angle at  and the side lengths of  and  was not enough to define a unique triangle, but knowing the angle at  and the side lengths of  and  would be enough to define a unique triangle.