4.3

147 Views

Download Presentation
## 4.3

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**4.3**What Makes Triangles Similar? Pg. 12 Conditions for Triangle Similarity**4.3–What Makes Triangles Similar?**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.**4.21 – 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? Corresponding angles must be congruent b. What must be true about their sides? Corresponding sides must be proportional**b. Measure the angles and sides of Erica's Triangles and**help her decide if the triangles are similar or not. 40° 5.6cm 2cm 20° 120° 40° 4.3cm 11.2cm 4cm 120° 20° 8.6cm Similar**4.22 – 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.**http://hotmath.com/util/hm_flash_movie_full.html?movie=/hotmath_help/gizmos/triangleSimilarity.swf**http://hotmath.com/util/hm_flash_movie_full.html?movie=/hotmath_help/gizmos/triangleSimilarity.swf http://hotmath.com/util/hm_flash_movie_full.html?movie=/hotmath_help/gizmos/triangleSimilarity.swf**Side-Side-Side Similarity:**If all 3 corresponding sides are proportional, then the triangles are similar E B A C D F**Angle-Angle Similarity:**If 2 corresponding angles are congruent, then the triangles are similar E B A C D F**4.23 – WHAT'S YOUR ANGLE?**Determine whether the triangles are similar. If they are, explain why and write a similarity statement.**77°**55° AA~**47°**31°**4.24 – ARE THEY SIMILAR?**Based on your conclusions, decide if each pair of triangles below are similar. If they are make a similarity statement. Then determine if you are using Angle-Angle similarity or Side-Side-Side similarity.**52°**96° AA~**d.**AA~ Yes,**4.25 – FLOWCHARTS**Examine the triangles at right. a. Are these triangles similar? Why? Yes, AA~**b. Julio decided to use a diagram (called a flowchart) to**explain his reasoning. Compare your explanation to Julio's flowchart. Did Julio use the same reasoning you used? Yes**c. What appears to go in the bubbles of a flowchart? What**goes outside the bubbles? Inside: Statements Outside: Reasons**4.26 – WRITING FLOWCHARTS**Besides showing your reasoning, a flowchart can be used to organize your work as you determine whether or not triangles are similar. a. Are these triangles similar? Why? Yes, SSS~**b. What facts must you know to use the triangle similarity**conjecture you chose? Julio started to list the facts in a flowchart at right. Complete the third oval.**c. Once you have the needed facts in place, you can**conclude that you have similar triangles. Add to your flowchart by making an oval and filling in your conclusion.**d. Finally, draw arrows to show the flow of the facts that**lead to your conclusion and record the similarity conjecture you used, following Julio's example.**4.27 – START FROM SCRATCH**a. What is the best conjecture to test for these triangles? SSS~ or AA~? AA~, Only know angles**b. Are these triangles similar? Justify your conclusion**using a flow chart.**given**ΔJKL ~ ΔYZX AA~**4.27 – HOW MANY OVALS?**a. What is the best conjecture to test for these triangles? SSS~ or AA~? SSS~, Only know sides**b. Are these triangles similar? Justify your conclusion**using a flow chart.**12**8 3 2 9 6 3 2 15. 10 3 2 = = = given given given ΔABC ~ ΔDEF SSS~