1 / 6

Methods of Proving Triangles Similar

Methods of Proving Triangles Similar. Lesson 8.3. Postulate: If there exists a correspondence between the vertices of two triangles such that the three angles of one triangle are congruent to the corresponding angles of the other triangle, then the triangles are similar. (AAA).

marie
Télécharger la présentation

Methods of Proving Triangles Similar

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Methods of Proving Triangles Similar Lesson 8.3

  2. Postulate: If there exists a correspondence between the vertices of two triangles such that the three angles of one triangle are congruent to the corresponding angles of the other triangle, then the triangles are similar. (AAA) The following 3 theorems will be used in proofs much as SSS, SAS, ASA, HL and AAS where used in proofs to establish congruency.

  3. Theorem 62: If there exists a correspondence between the vertices of two triangles such that two angles of one triangle are congruent to the corresponding angles of the other, then the triangles are similar. (AA) (no choice) Theorem 63: If there exists a correspondence between the vertices of two triangles such that the ratios of the measures of corresponding sides are equal, then the triangles are similar. (SSS~)

  4. Theorem 64: If there exists a correspondence between the vertices of two triangles such that the ratios of the measures of two pairs of corresponding sides are equal and the included angles are congruent, then the triangles are similar. (SAS~)

  5. Given: ABCD is a Prove: ∆BFE ~ ∆ CFD D C F E A B • ABCD is a • AB ║ DC • CDF  E • DFC  EFB • ∆ BFE ~ ∆CFD • Given • Opposite sides of a are ║. • ║ lines → alt. int. s • Vertical sare  • AA (3, 4)

  6. L Given: LP  EAN is the midpoint of LP. P and R trisect EA. Prove: ∆PEN ~ ∆PAL N A E P R Since LP  EA, NPE and LPA are congruent right angles. If N is the midpoint, of LP, NP = 1 . LP 2 But P and R trisect EA so EP = 1 . PA 2 Therefore, ∆PEN ~ ∆PAL by SAS ~.

More Related