Match the definition to the correct vocabulary word.Two pairs of proportional sides and a pair of equal included angles determine similar triangles.Answer 1 Question 57If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.Answer 2 Question 57If all three pairs of sides of corresponding triangles are in proportion, the triangles are similar.Answer 3 Question 57
Question
Match the definition to the correct vocabulary word.Two pairs of proportional sides and a pair of equal included angles determine similar triangles.Answer 1 Question 57If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.Answer 2 Question 57If all three pairs of sides of corresponding triangles are in proportion, the triangles are similar.Answer 3 Question 57
Solution
The definitions match the vocabulary words as follows:
Answer 1 Question 57: This definition matches the vocabulary word "Angle-Angle (AA) Similarity Postulate". This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Answer 2 Question 57: This definition matches the vocabulary word "Side-Side-Side (SSS) Similarity Theorem". This theorem states that if the lengths of all corresponding sides of two triangles are proportional, then the triangles are similar.
Answer 3 Question 57: This definition matches the vocabulary word "Side-Angle-Side (SAS) Similarity Theorem". This theorem states that if an angle of one triangle is congruent to an angle of a second triangle, and the lengths of the sides including these angles are in proportion, then the triangles are similar.
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Name the triangle congruence test described by each statement.a Two consecutive angles and a side length are equal.b Corresponding side lengths are equal.c Two pairs of corresponding angles and an included side are equal.d Have right angles and equal length of hypotenuse and another side.e Two corresponding sides and included angles are equal.
Introductory Activity for congruency of trianglesDear Students, This vacation you will discover all about congruency by yourself!Two triangles are said to be congruent when the 3 sides and 3 angles of one triangle isexactly equal to the 3 sides and 3 angles of another triangle.If you observe the above triangles, the 3 sides and 3 angles of △ABC is exactly equal to 3sides and 3 angles of △DFE. This means △ABC is congruent to △DFE.We write it as △ABC ≅ △DFEACTIVITYAim:It is sufficient if I can show that the 3 sides of one triangle is equal 3 sides of anothertriangle.The 3 angles of both the triangles become automatically equal.The two triangles are congruent.Procedure:Have students cut straws into the following lengths:2 straws 8 centimeters in length2 straws 11 centimeters in length2 straws 5 centimeters in length
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