University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

453

Pages:

3
Author:

Yasmine Burch

Congruent Polygons In your own words, write the meaning of each vocabulary term. corresponding parts ... in congruent polygons ... so if all sides are congruent and all angles are congruent, then we can say that we have congruent polygons. all congruent angles all congruent sides Theorem 5.3 Properties of Triangle Congruence Triangle congruence is reflexive, symmetric, and transitive. Reflexive: For any triangle ΔABC ≅ ΔABC (congruent to itself) Symmetric: If ΔABC ≅ ΔDEF then ΔDEF ≅ ΔABC Transitive: If ΔABC ≅ ΔDEF and ΔDEF ≅ ΔJKL then ΔABC ≅ ΔJKL (aka. Substitution) Theorem 5.4 Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. (already covered this in Ch6; Similarity) Since each triangle ... 180 = ∠A + ∠B + ∠C 180 = ∠D + ∠E + ∠F Combine them with substitution ... since both = 180 ∠A + ∠B + ∠C = ∠D + ∠E + ∠F -∠A -∠B -∠A - ∠B ...subbing in the angles we know that are congruent. ∠C = ∠F The last set of angles have to be congruent too. 5.2 Extra Practice In Exercises 1 and 2, identify all pairs of congruent corresponding parts. Then write another congruence statement for the polygons. (follow the name!) ΔPQR ≅ ΔSTU Angles: ∠P ≅ ∠S ∠Q ≅ ∠T ∠R ≅ ∠U Sides: PQ ≅ ST QR ≅ TU PR ≅ SU ABCD ≅ EFGH Angles: ∠A ≅ ∠E ∠B ≅ ∠F ∠C ≅ ∠G ∠D ≅ ∠H Sides: AB ≅ EF BC ≅ FG CD ≅ GH DA ≅ HE In Exercises 3 and 4, find the values of x and y. ΔXYZ ≅ ΔRST 15 = 3y + 9 -9 -9 6 = 3y / 3 2 = y 30 = 2x - 20 +20 +20 50 = 2x /2 25 = x ABCD ≅ EFGH 60 + 8x = 108 -60 -60 8x = 48 /8 x = 6 62 = 8y - 3x 62 = 8y -3(6) 62 = 8y -18 +18 +18 80 = 8y / 8 10 = y In Exercises 5 and 6, show that the polygons are congruent. Explain your reasoning. If ... sides and angles are all congruent. AB ≅ CB AD ≅ CD DB ≅ DB (reflective) ∠A ≅ ∠C ∠ADB ≅ ∠CDB ∠DBC ≅ ∠DBA (by third angle) So ΔABD ≅ ΔCBD NK ≅ IH KL ≅ JG LM ≅ GH MN ≅ IJ ∠L ≅ ∠J ∠M ≅ ∠I ∠N ≅ ∠H ∠K ≅ ∠G So MNKL ≅ IJGH (*each part is in order of connections) In Exercises 7 and 8, find m∠1. Draw the separate triangles 180 = 90 + 33 + ∠C -90 -90 -33 57 = ∠C 57+∠1 = 90 -57 -57 ∠1 = 33 180 = 80 + 54 + ∠1 -80 -80 -54 46 = ∠1