Lesson 5-2 Congruent Polygons.

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Presentation transcript:

Lesson 5-2 Congruent Polygons

Objectives Identify and use corresponding parts Use the Third Angles Theorem

Vocabulary Corresponding parts – corresponding parts map onto each other from a rigid motion mapping or from a statement of congruence or similarity by order CPCTC – Corresponding Parts of Congruent Triangles are Congruent

Congruent Triangles Order Rules!!! – When matching congruent statements: △DEF is the image of △ABC or △DEF  △ABC, order of appearance tells you which parts are corresponding. 3 angles congruent to 3 angles and 3 sides congruent to 3 sides

Triangle Theorems Like angles and segments, triangles have Reflexive, Symmetric and Transitive properties of congruence

Triangle Theorems Since all three angles in any triangle always add to 180, this theorem is really another corollary to the Angle Sum Theorem from lesson 5-1.

Example 1 Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts (sides and angles) Answer: Sides: Angles: MN  YX MP  YZ PN  ZX M  Y  P   Z  N   X

Example 2a In the diagram, ◊DEFG  ◊QMNP Find the value of x. Find the value of x. Answer: MQ corresponds to ED x – 2 = 8 x = 10

Example 2b In the diagram, ◊DEFG  ◊QMNP Find the value of y. Find the value of y. Answer: P corresponds to G 3x + 2y = 84 but x = 10 from part a 30 + 2y = 84 2y = 54 y = 27

Example 3 Show that ABD  CDB. Explain your reasoning Answer: For two triangles to be congruent, 3 sides and 3 angles must be congruent. Two angles are marked congruent and the third angle is congruent because of a hidden feature of parallel sides, alternate interior angles. Two sides are marked congruent and the third side is congruent because of a hidden feature of shared sides (reflexive property)

Example 4 Find 𝒎∠𝑷. Answer: Angle R congruent (equal) to angle A 180 = sum of triangle’s angles 180 = 90 + 52 + P 180 = 142 + P 38 = P

Example 5 Use the information in the figure to prove that ∆𝑾𝑿𝒀≅∆𝒁𝑽𝒀 Answer: Statement Reason XW  VZ Marked in picture XY  VY Marked in picture WY  ZY Marked in picture X  V All right angles congruent Y  Y Vertical angles congruent W  Z Third angle Thrm ∆𝑾𝑿𝒀≅∆𝒁𝑽𝒀 All angles and sides congruent

Summary & Homework Summary: Homework: Triangles can be classified by their angles as acute, obtuse or right Triangles can be classified by their sides as scalene, isosceles or equilateral Exterior angle = sum of remote interiors Interior angles sum to 180 Exterior angles sum to 360 Homework: Triangle Classification WS