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Section 8.4 Opening Act

In this lesson, you will learn about triangle similarity and how to establish congruence of angles and segment proportionality. Explore the concept of similarity, reasoning, and proportionality in triangles. Understand the theorem for similar triangles and apply it to solve proportionality problems. Develop your skills in working with formal geometry words and proofs. Practice shadow problems involving similar triangles formed by objects, rays, and shadows. By the end, you will be able to confidently analyze similarity in triangles and solve related problems.

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Section 8.4 Opening Act

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  1. A E F B C D Section 8.4Opening Act YES No-Choice Theorem AAA ABC ~ FED Are these triangles similar? Name two reasons to support your answer. If similar, state the corresponding vertices?

  2. A E D B F C Try Again YES If sides, then angles AAA or SAS~ ABC ~ EDF Are these triangles similar? Name two reasons to support your answer. If similar, state the corresponding vertices?

  3. E A B C D F Try Again YES SSS~ ABC ~ FED 1:2 Are these triangles similar? Name one reason to support your answer. If similar, state the corresponding vertices? If similar, what is the ratio?

  4. Section 8.4 Congruence/Proportion • By the end of this lesson you will be able to: • Use the concept of similarity to establish the congruence of angles and the proportionality of segments

  5. Section 8.4: Formal Words D A F E B C Statement Reason Corr. sides of ~ s are proportional. Means-Extremes Products Theorem

  6. Intermission If two similar kites have perimeters of 21 and 28, what is the ratio of the measures of two corresponding sides?

  7. Shadow Problems You notice a certain tree is casting a 30-m shadow. A nearby flagpole is casting a 24-m shadow. If the flagpole is 20 m high, how tall is the tree? What you need to know is that because the sun is soooooooo far away: The sun’s rays strike objects at the same angle. The sun’s rays are nearly parallel. Therefore you can use AA, and the similar triangles formed by the object, the ray, and the shadow.

  8. O S R N T P Prove It

  9. 8 A B 6 4 C 15 10 E D 20 Prove It

  10. G F E H D A B C Prove It

  11. Homework ?

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