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,

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Presentation transcript:

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 Side 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 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? Side Angle Side

SSA 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? Side Side Angle

ASA 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? Angle Side Angle

AAS 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? Angle Angle Side