Triangle Congruence: SSS, SAS, ASA, AAS, and HL Geometry 4.4 and 4.5 Triangle Congruence: SSS, SAS, ASA, AAS, and HL

Learning Targets Students should be able to… Apply SSS, SAS, ASA, AAS, and HL to construct triangles and to solve problems Prove triangles congruent by using SSS, SAS, ASA, AAS, and HL.

Warm-up #1

Homework Check

Homework Check

Homework Check

Homework Check

4.1 – 4.3 Quiz

Vocabulary Term Name Diagram Additional Notes Included angle ∠𝐵 𝑖𝑠 𝑡ℎ𝑒 𝑖𝑛𝑐𝑙𝑢𝑑𝑒𝑑 𝑎𝑛𝑔𝑙𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑖𝑑𝑒𝑠 𝐴𝐵 𝑎𝑛𝑑 𝐵𝐶 -an angle formed by two adjacent sides of a polygon C B A

Vocabulary Term Name Diagram Additional Notes Included angle ∠𝐵 𝑖𝑠 𝑡ℎ𝑒 𝑖𝑛𝑐𝑙𝑢𝑑𝑒𝑑 𝑎𝑛𝑔𝑙𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑖𝑑𝑒𝑠 𝐴𝐵 𝑎𝑛𝑑 𝐵𝐶 -an angle formed by two adjacent sides of a polygon Included side 𝑃𝑄 𝑖𝑠 𝑡ℎ𝑒 𝑖𝑛𝑐𝑙𝑢𝑑𝑒𝑑 𝑠𝑖𝑑𝑒 𝑜𝑓 ∠𝑃 𝑎𝑛𝑑 ∠Q -a common side of two consecutive angles in a polygon. C B A P Q R

Postulate 4-4-1 Side-Side-Side (SSS) Hypothesis Conclusion If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent. ∆ 𝐴𝐵𝐶≅∆𝐹𝐷𝐸 B C A D F E

Postulate 4-4-2 Side-Angle-Side (SAS) Hypothesis Conclusion If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle , then the triangles are congruent. ∆ 𝐴𝐵𝐶≅∆𝐹𝐷𝐸 B C A D F E

Postulate 4-4-3 Angle-Side-Angle (ASA) Hypothesis Conclusion 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. ∆ 𝐴𝐵𝐶≅∆𝐹𝐷𝐸 B C A D F E

Postulate 4-4-4 Angle-Angle-Side (AAS) Hypothesis Conclusion 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. ∆ 𝐴𝐵𝐶≅∆𝐹𝐷𝐸 B C A D F E

Review of Right Triangle Vocabulary Hypotenuse Leg C B Leg Right Angle

Postulate 4-5-3 Hypotenuse-Leg (HL) Hypothesis Conclusion If the hypotenuse and a leg of a right triangle are congruent to a hypotenuse and a leg of another right triangle, then the triangles are congruent. ∆ 𝐴𝐵𝐶≅∆𝐹𝐷𝐸 B C A D F E

Proof Time Given: 𝐴𝐷 ∥ 𝐸𝐶 , 𝐵𝐷 ≅ 𝐵𝐶 Prove: ∆𝐴𝐵𝐶≅∆𝐸𝐵𝐶 A D Statements Reasons B C D

Proof Time Given: ∠𝐵≅∠𝐶, ∠𝐷≅∠𝐹 M is the midpoint of 𝐷𝐸 Prove: ∆𝐵𝐷𝑀≅∆𝐶𝐹𝑀 C B Statements Reasons D M F

On your own!

Re-teach (Extra Problems if needed) 4-4

Re-teach (Extra Problems if needed) 4-4

Re-teach (Extra Problems if needed) 4-4

Re-teach (Extra Problems if needed) 4-4

Re-teach (Extra Problems if needed) 4-5

Re-teach (Extra Problems if needed) 4-5

Re-teach (Extra Problems if needed) 4-5

Re-teach (Extra Problems if needed) 4-5