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Lesson 8.4 & 8.5 Similar Triangles

Lesson 8.4 & 8.5 Similar Triangles. M. 33. L. 106 o. N. 20. 38 o. Q. 30. P. 36 o. Example. D LMN ~ D PQN Write a proportion of the side lengths. Find. M. 33. L. 106 o. N. 20. 38 o. Q. 30. P. 36 o. Using similarity. D LMN ~ D PQN Find MN. B. Q. A. P. C. R.

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Lesson 8.4 & 8.5 Similar Triangles

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  1. Lesson 8.4 & 8.5Similar Triangles

  2. M 33 L 106o N 20 38o Q 30 P 36o Example DLMN ~ DPQN Write a proportion of the side lengths. Find

  3. M 33 L 106o N 20 38o Q 30 P 36o Using similarity DLMN ~ DPQN Find MN

  4. B Q A P C R Postulate Angle-Angle Similarity (AA~) If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar if then

  5. Theorem Side-Side-Side Similarity (SSS~) If the corresponding sides of two triangles are proportional, then the triangles are similar if B C then E A F D

  6. Theorem Side-Angle-Side Similarity (SAS~) If an angle of one triangle is congruent to an angle of another triangle and the lengths of the sides that include these angles are proportional, then the triangles are similar if B C E then A F D

  7. B 18 15 A C 6 L 30 7 P Q 5 N M 3 10 25 R Example Use AA~ SSS~ SAS~ To choose the Similar Triangles

  8. Example A Given:AC= 6, AD = 10, BC = 9, BE = 15 Prove:DACB~ DDCE 6 E 6 C 4 9 B D It is given that AC = 6 and AD =10. DC = 4 and EC = 6by the Segment Addition Postulate and so by the Vertical Angles Theorem. Therefore by SAS~.

  9. Example Use similar triangles to find the width of the river. 26.25 ft 8 ft 42 ft 5 ft

  10. Proving Similar Triangles AA~ Show two pairs of corresponding angles are congruent SSS~ Show the side lengths are proportional SAS~ Show two pairs of corresponding sides are proportional and that the angles between the sides are congruent.

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