Concept Byte: Building Congruent Triangles

Use With Lesson 4-2

ACTIVITY

Can you use shortcuts to find congruent triangles? Find out by building and comparing triangles.

Activity 1

Step 1 Cut straws into three pieces of lengths 4 in., 5 in., and 6 in. Thread a string through the three pieces of straw. The straw pieces can be in any order.

Step 2 Bring the two ends of the string together to make a triangle. Tie the ends to hold your triangle in place.

Step 3 Compare your triangle with your classmates’ triangles. Try to make your triangle fit exactly on top of the other triangles.

1. Is your triangle congruent to your classmates’ triangles?
2. Make a Conjecture What seems to be true about two triangles in which three sides of one are congruent to three sides of another?
3. As a class, choose three different lengths and repeat Steps 1–3. Are all the triangles congruent? Does this support your conjecture from Question 2?

Activity 2

Step 1 Use a straightedge to draw and label any Δ A B C cap delta eh b c  on tracing paper.

Step 2 Use a ruler. Carefully measure A B ¯ eh b bar  and A C ¯ . eh c bar , .  Use a protractor to measure the angle between them, ∠ A . angle eh .

Step 3 Write the measurements on an index card and swap cards with a classmate. Draw a triangle using only your classmate's measurements.

Step 4 Compare your new triangle to your classmate's original Δ A B C . cap delta eh b c .  Try to make your classmate's Δ A B C cap delta eh b c  fit exactly on top of your new triangle.

4. Is your new triangle congruent to your classmate's original Δ A B C ? cap delta eh b c question mark
5. Make a Conjecture What seems to be true about two triangles when they have two congruent sides and a congruent angle between them?
6. Make a Conjecture At least how many triangle measurements must you know in order to guarantee that all triangles built with those measurements will be congruent?

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