8 3 Similar Triangles
- 1. Similar Triangles Focus – Apply the properties of similar triangles and tomorrow, prove that triangles are similar. Lesson 8-3 WA State Standards: G.3.A and G.3.B
- 2. Congruent Triangles …have matching angles that are congruent. …have matching sides that are congruent. A B C D F E 100° 35° 45° 115 ft 150 ft 100 ft 150 ft 115 ft 100 ft 35° 100° 45°
- 3. Congruent Triangles …have matching angles that are congruent. …have matching sides that are congruent. A B C D F E 100° 35° 45° 115 ft 150 ft 100 ft 150 ft 115 ft 100 ft 35° 100° 45°
- 4. Similar Triangles IF and ONLY IF Vertices match up so corresponding angles are congruent. Corresponding sides are in proportion . 30° 30° 75° 75° 75° 75° 16 12 12 16 6 8 Ratios of each side are
- 5. Triangle Similarity Postulate If two angles of one triangle are equal in measure to two angles of another triangle, then the two triangles are similar . AA (angle/angle) similarity
- 6. AA? You will also see: SAS ASA SSS Knowing these letters will help with proofs later . Side/Angle/Side Angle/Side/Angle Side/Side/Side
- 7. Are they similar? Only one angle is given as congruent. Two must be given to use Angle/Angle or AA Similarity .
- 8. Are they similar? Use Angle/Angle or AA Similarity . Two congruent angles show triangles are similar.
- 9. Similar? Find the missing side of each triangle to find two 30° angles and a 120° angle for each of these similar triangles. 120° 30° 30° 30°
- 10. Is ABC similar to AEF? A E F C B Sometimes it helps to separate the two triangles and look at each angle separately.
- 11. Find the missing side We previously determined that these triangles are similar . We can set up ratios to find the missing side. Start with a label on top and bottom. 120° 30° 30° 30° 7 ft 21 ft 28 ft n ft
- 12. In today’s lesson… We found that congruent triangles have both congruent angles and sides. Similar triangles have congruent angles. We can use the AA similarity to determine if triangles are similar. We can use ratios to determine a missing side’s length when similar triangles are used. WA State Standards: G.3.A and G.3.B
- 13. Assign: 453: 4-8; 12-13 457: 1-4 This statue can be seen in downtown Seattle in the Pacific Place Mall on the main level.
- 14. Day Two Yesterday, we found that…. We found that congruent triangles have both congruent angles and sides. Similar triangles have congruent angles. We can use the AA similarity to determine if triangles are similar. Today’s Focus- Prove that triangles are similar.
- 15. Overlapping Triangles It is sometimes useful to redraw as separate triangles to name the congruent sides and angles of those triangles. A C B A F E
- 16. Is ABC similar to AEF? If so, what Is the missing side? y 15 16 x 12 12 A B C E F
- 17. It often helps to separate the two attached triangles. y 15 16 x 12 12
- 18. Prove: A line drawn from a point on one side of a triangle parallel to another side forms a triangle similar to the original triangle.
- 19. Did you notice that the words corresponding occur with parallel lines and triangles? Corresponding Angles in triangles are different than when working with parallel lines, but in both cases are congruent. WARNING
- 20. Given: ; Prove: 1. 2. 3. Given If two || lines are intersected by a transversal, then corresponding angles are = in measure AA Similarity
- 21. 9. Given: Prove: 1. 2. 3. 1.Given 2.Alternate Interior Angles from Transversal/Parallel Lines Theorem 3.AA Similarity Postulate A E D B C
- 22. Overlapping Similar Triangles Theorem If a line is drawn from a point on one side of a triangle parallel to another side, …then it forms a triangle similar to the original triangle.
- 23. Solve by using proportions 4 ft 6 ft 5 ft x
- 24. Assign: 453: 9; 14, 16, 21a, 23, 26 457: 5-7