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Transcript

Notes 4.5/4.6 Geometry Pre-AP Yesterday, you learned 2 shortcuts for proving triangles congruent. Use either the SSS or the SAS shortcut to prove the following triangles congruent. Statements Reasons There are 3 more shortcuts that are valid and can be used to prove two triangles congruent! Angle-Side-Angle (ASA) Congruence Postulate Picture Congruence Statement If two angles and the Included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. **ASA stands for two angles and the _______________ side. Example: 1. Determine if you can use ASA to prove UVX WVX. Explain! Also, what transformation takes place to change position from one triangle to the orientation of the second triangle? Angle-Angle-Side (AAS) Congruence Postulate Picture Congruence Statement If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent. Example: 2. DIG DEEPER: Is AAS the only way to prove these triangles congruent on the problem above? If not, then what other conjecture could we use? Hypotenuse-Leg (HL) Congruence Postulate Picture Congruence Statement If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another triangle, then the triangles are congruent. This method of proof CANNOT be used unless you first prove the triangles are Right! Examples: Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know! 3. VWX and YXW 4. VWZ and YXZ Section 4.6 Once we have proven that two triangles are congruent, then we know that every other “piece” of the triangles is ALSO congruent. Example: If I know that ABC RST by _________, then A must be congruent to R also. A R 12 B 58º 10 Given: PR bisects C S 58º QPS and QRS Prove: PQ PS Given: Prove: This is because Corresponding Parts of Congruent Triangles are Congruent or 12 YW bisects XZ , XY YZ XYW ZYW 10 T