4.4 What Information Do I need? Pg. 14 Conditions for Triangle Similarity.

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4.4 What Information Do I need? Pg. 14 Conditions for Triangle Similarity

4.5–What Information Do I Need? Conditions for Triangle Similarity Now that you know what similar shapes have in common, you are ready to turn to a related question: How much information do I need to know that two triangles are similar? As you work through today's lesson, remember that similar polygons have corresponding angles that are equal and corresponding sides that are proportional.

4.26 – ARE THEY SIMILAR? Erica thinks the triangles below might be similar. However, she knows not to trust the way figures look in a diagram, so she asks for your help.

a. If two shapes are similar, what must be true about their angles? Their sides? Corresponding angles must be congruent Corresponding sides must be proportional

120° 20° 40° 11.2cm 5.6cm 4cm 2cm 8.6cm 4.3cm b. Measure the angles and sides of Erica's Triangles and help her decide if the triangles are similar or not.

4.27 – HOW MUCH IS ENOUGH? Jessica is tired of measuring all the angles and sides to determine if two triangles are similar. "There must be an easier way," she thinks. "What if I know that all of the side lengths have a common ratio? Does that mean that the triangles are similar?"

a. Before experimenting, make a prediction. Do you think that the triangles have to be similar if the pairs of corresponding sides share a common ratio?

b. Experiment with Jessica's idea. To do this, use either a manipulative or dynamic geometry tool to test triangles with proportional side lengths. Can you create two triangles that are not similar? h_help/gizmos/triangleSimilarity.swf

c. Jessica then asks, "Is it enough to know that each pair of corresponding angles are congruent? Does that mean the triangles are similar?" Again, make a prediction, test this claim use either a manipulative or dynamic geometry tool to test triangles with equal corresponding angles. Can you create two triangles with the same angle measures that are not similar? help/gizmos/triangleSimilarity.swf

a. Are the corresponding angles equal? Convince Scott that these triangles are similar by finding the missing angles. 25° 68°

b. How many pairs of angles need to be congruent to be sure that triangles are similar? 25° 68° You only need to know 2 angles!!!

vertical angles are = by AA~

4.29 – ARE THEY SIMILAR? Based on your conclusions, decide if each pair of triangles below are similar. Explain your reasoning by stating which angles are equal OR which sides have the same ratio. Then determine if you are using Angle- Angle similarity or Side-Side-Side similarity.

by SSS~

96° 52° AA~

d. Yes, AA~