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Enriched PreAlgebra Congruent Polygons (Chapter 65) Course 3 Congruent Polygons6‐5 (a of b) G1: Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures. G4: Determine necessary conditions for congruence of triangles. Polygons that have the EXACT same size and shape are called ___________________ polygons. Remember that the parts of two polygons that match or go together 2. Determine whether the trapezoids shown are congruent. If so, name the corresponding parts and write a congruence statement. are called ___________________________. So, if two polygons are congruent, then we know that their corresponding ______________ are _______________ and their corresponding _____________ are congruent. 1. Determine whether the triangles shown are congruent. If so, name the corresponding parts and write a congruence statement. 3. In the figure, FGH QRS. Name the corresponding parts, means to name ALL of the corresponding parts‐ the ANGLES AND THE SIDES!!!! A. Find the measure of angle F: _______ B. Find the measure of angle S: _______ C. SR D. QS 1 Enriched PreAlgebra Congruent Polygons (Chapter 65) Course 3 Congruent Polygons6‐5 (a of b) G1: Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures. G4: Determine necessary conditions for congruence of triangles. Polygons that have the EXACT same size and shape are called ___________________ polygons. Remember that the parts of two polygons that match or go together 2. Determine whether the trapezoids shown are congruent. If so, name the corresponding parts and write a congruence statement. are called ___________________________. So, if two polygons are congruent, then we know that their corresponding ______________ are _______________ and their corresponding _____________ are congruent. 1. Determine whether the triangles shown are congruent. If so, name the corresponding parts and write a congruence statement. 3. In the figure, FGH QRS. A. Find the measure of angle F: _______ Name the corresponding parts, means to name ALL of the corresponding parts‐ the ANGLES AND THE SIDES!!!! B. Find the measure of angle S: _______ C. SR D. QS 2 Enriched PreAlgebra Congruent Polygons (Chapter 65) Course 3 Congruent Polygons6‐5 (a of b) G1: Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures. G4: Determine necessary conditions for congruence of triangles. Polygons that have the EXACT same size and shape are called ___________________ polygons. Remember that the parts of two polygons that match or go together 2. Determine whether the trapezoids shown are congruent. If so, name the corresponding parts and write a congruence statement. are called ___________________________. So, if two polygons are congruent, then we know that their corresponding ______________ are _______________ and their corresponding _____________ are congruent. 1. Determine whether the triangles shown are congruent. If so, name the corresponding parts and write a congruence statement. 3. In the figure, FGH QRS. A. Find the measure of angle F: _______ Name the corresponding parts, means to name ALL of the corresponding parts‐ the ANGLES AND THE SIDES!!!! B. Find the measure of angle S: _______ C. SR D. QS 3 Enriched PreAlgebra Congruent Polygons (Chapter 65) Course 3 Congruent Polygons‐ Triangles6‐5 (b of b) G1: Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures. G4: Determine necessary conditions for congruence of triangles. Now that we have learned about the congruence of polygons‐ there’s even more that we can learn about the congruence of one special polygon. There are certain ways that triangles can be congruent. What we cover today ONLY applies to triangles‐ but it WILL make your life easier! _____________________________________ If three sides of one triangle are congruent to three sides of a second triangle, the two triangles are congruent. 1. Are these two triangles congruent? Explain. _______________________________________ When you know the side length , then the next angle measure, and the next side length of two triangles are exactly the same, then you know that those two triangles are congruent! 2. Are these two triangles congruent? Explain. If two sides and the included angle are congruent to two sides and the included angle of a second triangle, the two triangles are congruent. ________________________________ 3. Are these two triangles congruent? Explain. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. 4 Enriched PreAlgebra Congruent Polygons (Chapter 65) Course 3 Congruent Polygons‐ Triangles6‐5 (b of b) G1: Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures. G4: Determine necessary conditions for congruence of triangles. Now that we have learned about the congruence of polygons‐ there’s even more that we can learn about the congruence of one special polygon. There are certain ways that triangles can be congruent. What we cover today ONLY applies to triangles‐ but it WILL make your life easier! _____________________________________ If three sides of one triangle are congruent to three sides of a second triangle, the two triangles are congruent. 1. Are these two triangles congruent? Explain. _______________________________________ When you know the side length , then the next angle measure, and the next side length of two triangles are exactly the same, then you know that those two triangles are congruent! 2. Are these two triangles congruent? Explain. If two sides and the included angle are congruent to two sides and the included angle of a second triangle, the two triangles are congruent. ________________________________ 3. Are these two triangles congruent? Explain. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. 5 Enriched PreAlgebra Congruent Polygons (Chapter 65) Course 3 Congruent Polygons‐ Triangles6‐5 (b of b) G1: Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures. G4: Determine necessary conditions for congruence of triangles. Now that we have learned about the congruence of polygons‐ there’s even more that we can learn about the congruence of one special polygon. There are certain ways that triangles can be congruent. What we cover today ONLY applies to triangles‐ but it WILL make your life easier! _____________________________________ If three sides of one triangle are congruent to three sides of a second triangle, the two triangles are congruent. 1. Are these two triangles congruent? Explain. _______________________________________ When you know the side length , then the next angle measure, and the next side length of two triangles are exactly the same, then you know that those two triangles are congruent! 2. Are these two triangles congruent? Explain. If two sides and the included angle are congruent to two sides and the included angle of a second triangle, the two triangles are congruent. ________________________________ 3. Are these two triangles congruent? Explain. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. 6 Enriched PreAlgebra Congruent Polygons (Chapter 65) Course 3 Congruent Polygons6‐5 (a of b) G1: Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures. G4: Determine necessary conditions for congruence of triangles. Polygons that have the EXACT same size and shape are called ___________________ polygons. Remember that the parts of two polygons that match or go together 2. Determine whether the trapezoids shown are congruent. If so, name the corresponding parts and write a congruence statement. are called ___________________________. So, if two polygons are congruent, then we know that their corresponding ______________ are _______________ and their corresponding _____________ are congruent. 1. Determine whether the triangles shown are congruent. If so, name the corresponding parts and write a congruence statement. 3. In the figure, FGH QRS. Name the corresponding parts, means to name ALL of the corresponding parts‐ the ANGLES AND THE SIDES!!!! A. Find the measure of angle F: _______ B. Find the measure of angle S: _______ C. SR D. QS 7 Enriched PreAlgebra Congruent Polygons (Chapter 65) Course 3 Congruent Polygons‐ Triangles6‐5 (b of b) G1: Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures. G4: Determine necessary conditions for congruence of triangles. _____________________________________ Now that we have learned about the congruence of polygons‐ there’s even more that we can learn about the congruence of one special polygon. There are certain ways that triangles can be congruent. What we cover today ONLY applies to triangles‐ but it WILL make your life easier! If three sides of one triangle are congruent to three sides of a second triangle, the two triangles are congruent. 1. Are these two triangles congruent? Explain. _______________________________________ When you know the side length , then the next angle measure, and the next side length of two triangles are exactly the same, then you know that those two triangles are congruent! 2. Are these two triangles congruent? Explain. If two sides and the included angle are congruent to two sides and the included angle of a second triangle, the two triangles are congruent. 3. Are these two triangles congruent? Explain. ________________________________ If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. 8 Enriched PreAlgebra Congruent Polygons (Chapter 65) 9