1 / 20

CONGRUENT TRIANGLES

CONGRUENT TRIANGLES . How To Find Congruent Sides ? ?. Remember to look for the following:. Adjacent triangles share a COMMON SIDE , so you can apply the REFLEXIVE Property to get a pair of congruent sides .

finian
Download Presentation

CONGRUENT TRIANGLES

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. CONGRUENT TRIANGLES

  2. How To Find Congruent Sides ? ? • Remember to look for the following: • Adjacent triangles share a COMMON SIDE, so you can apply the REFLEXIVE Property to get a pair of congruent sides. • Look for segment bisectors.. They lead to midpoints…. Which lead to congruent segments.

  3. AB CD and BC  DA Given AC CA Reflexive Use SSS  to explain why ∆ABC  ∆CDA. ∆ABC ∆CDA SSS 

  4. An included angle is an angle formed by two adjacent sides of a polygon. B is the included angle between

  5. How To Find Congruent ANGLES ? ? • Remember to look for the following: • Look for VERTICAL ANGLES. • Look for lines. They form  adjacent angles. • Look for // LINES CUT BY A TRANSVERSAL. They lead to  angles. • Look for < bisectors. They lead to  angles.

  6. The letters SAS are written in that order because the congruent angles must be INCLUDED between pairs of congruent corresponding sides.

  7. XZ VZ YZ  WZ Given Engineering Application The diagram shows part of the support structure for a tower. Use SASto explain why ∆XYZ  ∆VWZ. XZY  VZW VERTICAL <‘s are  ∆XYZ  ∆VWZ SAS .

  8. An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.

  9. When using ASA  , the side must be INCLUDED between the angles known to be congruent.

  10. KL and NM are //. KLN MNL, because // lines imply  alt int >s. Determine if you can use ASA  to prove NKL LMN. Explain. NL  LN by the Reflexive Property. No other congruence relationships can be determined, so ASA cannot be applied.

  11. When using AAS  , the sides must be NONINCLUDED and opposite corresponding angles.

  12. Use AAS to prove the triangles  Given:JL bisects KLM K  M Prove:JKL  JML JL bisects KLM K  M Given JL  JL Reflexive KLJ MLJ Def. < bis. JKL  JML AAS 

  13. When using HL  , you must FIRST state that there is a RIGHT TRIANGLE!

  14. Determine if you can use the HL Congruence Theorem to prove ABC  DCB. AC DB Given ABC& DCB are right angles Given BC CB Reflexive ABC& DCBare rt. s Def. right   ABC  DCBHL.

  15. Ways to prove  triangles SSS SAS HL ASA AAS

More Related