Math 8 Term 3 AY 2022 - 2023 Triangle Congruence PDF

L3: CONDITIONS FOR TRIANGLE CONGRUENCE MATH 8 Term 3 AY 2022 - 2023 Week 5 | May 8 - 12, 2023 Ms. Alexa ,Ms. Melds, Sir Wilson Today's Learning Targets: I can illustrate triangle congruence. I can state SAS, SAS, and SSS congruence postulates; and SAA congruence the...

L3: CONDITIONS FOR TRIANGLE CONGRUENCE MATH 8 Term 3 AY 2022 - 2023 Week 5 | May 8 - 12, 2023 Ms. Alexa ,Ms. Melds, Sir Wilson Today's Learning Targets: I can illustrate triangle congruence. I can state SAS, SAS, and SSS congruence postulates; and SAA congruence theorem. I can illustrate SAS, SAS, and SSS congruence postulates; and SAA congruence theorem. I can solve corresponding parts of congruent triangles. Which of the following figures below have the same shape and size? Having the same shape and size means congruent and is denoted ≅. Geometric Transformations ROTATION - is when we rotate an image by a certain degree. Geometric Transformations REFLECTION – is when we flip the image along a line. The flipped image is called the mirror image. Geometric Transformations TRANSLATION – this happens when we move or slide the image without changing anything in it. Thus, the shape, size, and orientation remain the same. Correspondence A correspondence between two triangles is a pairing of each vertex with another one (and only one) vertex of another triangle. This pairing of vertices can be described by using the correspondence symbol, ↔. Thus, ∆𝐴𝐵𝐶 ↔ ∆𝐷𝐸𝐹, which means that A is paired with D, B with E, and C with F. Correspondence In the correspondence, ∆𝐴𝐵𝐶 ↔ ∆𝐷𝐸𝐹 There are three pairs of corresponding angles and three pairs of corresponding sides. These parts that correspond are called corresponding parts of the two triangles. Exercise 3.1 1.For each of the following, state which type of transformation is illustrated: Exercise 3.1 1. For each of the following, state which type of transformation is illustrated: Congruent Triangles Definition: Two triangles are congruent if and only if their corresponding parts are congruent. For instance, if ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹, then it follows that the corresponding parts are congruent.  SOLVING CORRESPONDING PARTS OF CONGRUENT TRIANGLES Suppose ∆𝐴𝐿𝐸 ≅ ∆𝑆𝑂𝑁, answer each of the following. 1. If LE = 3𝑥 + 19, and NO = 5𝑥 − 11, then what is the value of 𝑥?  SOLVING CORRESPONDING PARTS OF CONGRUENT TRIANGLES Suppose ∆𝐴𝐿𝐸 ≅ ∆𝑆𝑂𝑁, answer each of the following. 2. If 𝑚∠𝑆 = 2𝑥 + 5, and 𝑚∠𝐴 = 𝑥 + 30, then what is the 𝑚∠𝐴?  SOLVING CORRESPONDING PARTS OF CONGRUENT TRIANGLES Suppose ∆𝐴𝐿𝐸 ≅ ∆𝑆𝑂𝑁, answer each of the following. 3. If 𝑚∠𝐸 = 5𝑥 − 6, and 𝑚∠𝑁 = 2𝑥 + 15, then what is the 𝑚∠𝑁? 𝑚∠𝑆?  Exercise 3.4 Solve each.. Triangle Congruence Postulates & Theorem 1. SSS Congruence Postulate 2. SAS Congruence Postulate 3. ASA Congruence Postulate 4. SAA/AAS Congruence Theorem SSS Congruence Postulate (Side – Side – Side) If three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent. In the figure given, 𝐴𝐶 ≅ 𝑃𝑅 (side) 𝐴𝐵 ≅ 𝑃𝑄 (side) 𝐵𝐶 ≅ 𝑄𝑅 (side) hence, ∆𝑨𝑩𝑪 ≅ ∆𝑷𝑸𝑹, by SSS Congruence Postulate. SAS Congruence Postulate (Side – Angle – Side) If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent. Definition: An included angle is the angle formed of two adjacent sides of a triangle. ∠𝒀 is the included angle between the sides 𝑆𝑌 and 𝐾𝑌. SAS Congruence Postulate (Side – Angle – Side) If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent. ASA Congruence Postulate (Angle – Side – Angle) 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. Definition: An included side is the common side to two angles of a triangle. 𝑩𝑬 is the included side between ∠𝐵 and ∠𝐸. 𝑩𝑫 and 𝑫𝑬 are the non- included sides between ∠𝐵 and ∠𝐸. ASA Congruence Postulate (Angle – Side – Angle) 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. In the figure given, ∠𝑌 ≅ ∠𝐷 (angle) 𝑌𝑍 ≅ 𝐷𝐾 (included side) ∠𝑍 ≅ ∠𝐾 (angle) hence, ∆𝑨𝑩𝑪 ≅ ∆𝑰𝑫𝑲, by ASA Congruence Postulate. SAA/AAS Congruence Theorem If the two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent. In the figure given, ∠𝐴 ≅ ∠𝐷 (angle) ∠𝐶 ≅ ∠𝑍 (angle) 𝐴𝐵 ≅ 𝑋𝑌 (non-included side) hence, ∆𝑨𝑩𝑪 ≅ ∆𝑿𝒀𝒁, by SAA/AAS Congruence Theorem. Exercise 3.2 1.Determine if the two triangles are congruent. If they are, state what congruence postulate/theorem used: Exercise 3.2 1.Determine if the two triangles are congruent. If they are, state what congruence postulate/theorem used: Exercise 3.3 2. State what additional information is required in order to know that the triangles are congruent for a reason given. SSS ASA Exercise 3.3 2. State what additional information is required in order to know that the triangles are congruent for a reason given. SAS Self-Assess