B. Directions: Illustrate the congruent triangle using the given statements and mark the congruent parts then write the congruence postulate (ASA,SAS,SSS) used based in the given statement then proved. 7-10. (4pts.) If ZY~LM, LONZA, LU~ZN, then AYOU ~ AMAN triangle congruence postulate: 8-10. Draw your congruent triangle here 7.TRIANGLE CONGRUENCE Congruent Triangles Two triangles are congruent if and only if their corresponding parts (sides and angles) are congruent. This definition is abbreviated as CPCTC, which means Corresponding Parts of Congruent Triangles are Congruent. Illustrative Example 1 Given that AABC ~ ADEF (read as "Triangle ABC is congruent to triangle DEF"). Name the corresponding congruent sides and angles. Corresponding Angles Corresponding Sides LA ~ LD AB ~ ED LB ~ LE BC ~ FE LC ~ LF CA ~ FD Properties of Triangle Congruence Reflexive Property AXYZ ~ AXYZ D.D. Symmetric Property If AXYZ ~ AQRS, then AQRS ~ AXYZ. Transitive Property If AXYZ = AQRS and AQRS ~ AMNO, then AXYZ = AMNO D.D. .D. Triangle Congruence Postulates SSS (Side-Side-Side) Congruence Postulate If AB ~ DE, BC ~ EF and If the three sides of one triangle are congruent to the AC ~ DF, then three sides of another triangle, then the triangles are A ABC ~ DEF by SSS congruent. postulate. Often times called the side-side-side pattern. SAS (Side-Angle-Side) Congruence Postulate If AC ~ DF, LC ~ LF and If the two sides and an included angle of one triangle BC ~ EF, then are congruent to the corresponding two sides and the A ABC ~A DEF by SAS included angle of another triangle, then the triangles are postulate. congruent. "Included angle" is the angle formed by two given sides. ASA (Angle-Side-Angle) Congruence Postulate If LB ~ LE, BC ~ EF and If the two angles and the included side of one triangle LC ~ LF, then are congruent to the corresponding two angles and an A ABC ~A DEF by ASA included side of another triangle, then the triangles are B postulate. congruent. "Included side" is the side whose endpoints are the vertices of the angles. AAS (Angle-Angle-Side) Congruence Theorem If ZA ~ LD, LC ~ LF and If two angles and a non-included side of one triangle BC ~ EF, then are congruent to the corresponding two angles and a non- A ABC ~ DEF by AAS included side of another triangle, then the triangles are postulate. congruent.Example 1. Problem: Juan is planning to build a house with triangular roof structure. He wants to make this sketch perfect and accurate in terms of its measurement. He noticed that the roof structure is made up of two triangles. To say that the triangular structure must be perfect and accurate these triangles must have the same size and shape. Can we say that the triangles are congruent based on the sketch? Let A, B and D be the vertices e the vertices of the second triangle. Observe that if we separate the triangles BI Based on the markings, AB~CB AD=CD BD~BD because, BD is common to both triangles. Therefore, AABDZACBD by SSS Congruence Postulate Example 2 From the diagram, you know that BD ~ CD and AD = AD. The angle included between AD and BD is LBDA. The angle included between CD and AD is LCDA . Because any two right angles are congruent, _ BDA ~ ZCDA You can use the SAS Postulate to conclude that AADB ~ AADC. Example 3 In the figure, ZA ~LD, LB ~LE, and AC ~ PR. The ASA Postulate can be used to show that ABAC~ AEDC because AB and DE are included between B C E F the congruent angles. Example 4. In the figure, ZF ~LD, LE ~LB, and AF ~ BD. Therefore AFAE ~ ADBC by AAS Congruence Postulate. A A