Two triangles are congruent if and only if their corresponding parts are congruent. (CPCTC)
The seat and legs of this stool form two triangles. Suppose the measures in inches QR =12, RS =23, QS =24, RT =12, TV =24, and RV =23. A) Name the corresponding congruent angles and sides. B) Name the congruent triangles.
Show that the polygons are congruent by identifying all the congruent corresponding parts. Then write a congruence statement.
In the diagram, . Find the values of x and y. DFE ABC
Theorem 4.3 – Third Angles Theorem – If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.
The planners of the Senior Banquet decide to fold the dinner napkins using the Triangle Pocket Fold so that they can place a small gift in the pocket. If . , 40 , SRT m find NPQ m and RST NPQ
Write a two-column proof. Given: Prove: GFE DFE G D GF DF GE DE , , , GEF DEF
Theorem 4.4 – Congruence of triangles is reflexive, symmetric, and transitive.
Section 4-4 Proving Congruence SSS, SAS
I CAN…. • Use the SSS Postulate to test for triangle congruence. • Use the SAS Postulate to test for triangle congruence.
Postulate 4.1 – Side-Side-Side Congruence – If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. Abbreviation: SSS
Write a proof. Given: and L is the midpoint of Prove: , , JL HL KJ GH GK KJL GHL G J L H K
The tail of an orca whale can be viewed as two triangles that share a common side. Write a two-column proof to prove that if and . CYA BYA AC AB CY BY
Included Angle – In a triangle, the angle between two given sides. Included Angle
Postulate 4.2 – Side-Angle-Side Congruence – 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. Abbreviation: SAS
Write a two-column proof. Given: X is the midpoint of X is the midpoint of Prove: BXA DXC BD AC