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Download 10012314.2 Isosceles Triangles
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4.2 Properties of Isosceles Triangles Investigation 1 – Base Angles in an Isosceles Triangle Step 1: Draw an angle on patty paper. Lable it C. This angle will be the vertex angle of your isosceles triangle. Each member of your group needs to make a different angle. At least one member must draw an acute angle and at least one must draw an obtuse angle. All lines must be drawn with a straightedge. Step 2: Place a point A on one of the sides that make up the angle you have drawn. Fold your patty paper so that the two sides of the angle match up with each other. Step 3: Label the point on the other side of C that corresponds with point A, point B. Draw AB. You have constructed an isosceles triangle. Explain how you know that it is isosceles triangle using complete sentences. Name the base and the base angles. Name the legs. Step 4: Use your protractor to compare the measures of the base angles. What relationship do you notice? Fold the patty paper to confirm this relationship. Step 5: Based on your results complete the Isosceles Triangle Conjecture Isosceles Triangle Conjecture: If a triangle is isosceles, then _______________________________________________. Investigation 2 - Is the converse true? Step 1: Draw a segment and label it AB. Draw an acute angle with point A as the vertex. Each member of your group should draw a different angle. This angle will be a base angle of an isosceles triangle. Why can’t the base angle be obtuse? Step 2: Using your protractor draw an angle congruent to the one you drew in step 1 with point B as the vertex. If need be, extend the sides of the two angles that you have drawn until they intersect. Label the point of intersection, point C. Step 3: With a ruler measure the lengths of sides AC and BC. What relationship do you notice? Is this relationship true for everyone in your group? Step 4: Use your results to complete the conjecture below. Converse of the Isosceles Triangle Conjecture If a triangle has two congruent angles, then ____________________________________.
