Triangle Properties and Congruent Triangles Triangle Side Measures

Triangle Properties and Congruent Triangles

Triangle Side Measures • Try to make the following triangles with sides measuring: • 5 cm, 8 cm, 16 cm • 5 cm, 8 cm, 13 cm • 5 cm, 8 cm, 10 cm • 2 cm, 5 cm, 8 cm • With which three measures were you able to make a triangle? Why did the other measures not “work”?

Hinge Theorem • With your ruler construct an angle with sides measuring 10 cm and 7 cm. • Now construct another angle, NOT congruent to the first angle, with sides measuring 10 cm and 7 cm. • Connect the two sides of the angles to construct triangles. • Measure the angles and the third sides and form a conjecture about their relationship.

SSS Side • Construct a triangle. • Using the SAME side measures can you make a different triangle? • What happens to the sides when you try to change the angles? • How is this related to the Hinge Theorem?

SAS Side Angle Side • Construct an angle with the sides as Segments, not rays. • Can you make two different triangles? • Why or why not? Is your reasoning related to the Hinge Theorem?

SSA Side Angle • Construct a angle with extending one side as a ray and the other side as a segment. • Construct a circle with center at the endpoint of the segment that is NOT the vertex of the angle? • How many places does the circle intersect the ray? • How many triangles could you construct?

ASA Angle Side Angle • Construct two angles that share a side. That side has to be a segment. • Extend the two rays. Will the rays intersect in more than one place without changing the angles? • How many triangles can you construct?

AAS Angle Side • Construct a angle with extending one side as a ray and the other side as a segment. • Construct another angle with vertex anywhere along the ray. Will be able to make a triangle? Remember that the position does not make the angle. • Is there more than one place that you can place the angle and make a triangle?