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Corresponding Parts of Geometric Figures

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To name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS. In a congruence statement, the order of the vertices indicates the corresponding parts. Naming Figures

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Naming & Comparing Polygons List vertices in order, either clockwise or counterclockwise. When comparing 2 polygons, begin at corresponding vertices; name the vertices in order and; go in the same direction. By doing this you can identify corresponding parts. A D C B E DCBAE P I J K H IJKPH D corresponds to I AE corresponds to PH

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Name corresponding parts Name all the angles that correspond: A D C B E P I J K H D corresponds to I C corresponds to J B corresponds to K A corresponds to P E corresponds to H DCBAEIJKPH Name all the segments that correspond: DC corresponds to IJ CB corresponds to JK BA corresponds to KP AE corresponds to PH ED corresponds to HI How many corresponding angles are there? How many corresponding sides are there? 55

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How many ways can you name pentagon DCBAE? A D C B E 10 Do it. DCBAE CBAED BAEDC AEDCB EDCBA Pick a vertex and go clockwisePick a vertex and go counterclockwise DEABC CDEAB BCDEA ABCDE EABCD

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Polygon Congruence Postulate If each pair of corresponding angles is congruent, and each pair of corresponding sides is congruent, then the two polygons are congruent.

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Congruence Statements Given: These polygons are congruent. Remember, if they are congruent, they are EXACTLY the same. That means that all of the corresponding angles are congruent and all of the corresponding sides are congruent. DO NOT say that all the sides are congruent and all the angles are congruent, because they are not. G H F E C D B A CONGRUENCE STATEMENT ABCD = EFGH ~

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Examples

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When you write a statement such asABC DEF, you are also stating which parts are congruent. Helpful Hint

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Given: PQR STW Identify all pairs of corresponding congruent parts. Angles: P __, Q __, R __ Sides: PQ __, QR __, PR __ STW STTWSW Naming Congruent corresponding Parts

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1. ABC JKL and AB = 2x JK = 4x – 50. Find x and AB. Given that polygon MNOP polygon QRST, identify the congruent corresponding part. 2. NO ____ 3. T ____ 4. ABC EDC A __, AB __ B __, BC __ C __, AC __ 31, 74 RS P ED C ED EC DC More Practice

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Corresponding parts must also be written in order for similar polygons. Following the order of the statement allows you to set up proportions to solve for missing parts. Similar Polygons

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What do you notice about the sides of the above triangles? Practice

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Correspondence between two polygons –Corresponding angles are congruent –Lengths of the sides of the polygon are proportional List all of the pairs of the congruent angles. The ~ is used to show similarity More Similar Polygons

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D CB A E Writing Proportions using Corresponding Parts

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What is a scale factor –If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor What is the scale factor? W X Y B P QR S Scale Factor

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is called the scale factor Statement of proportionality Analysis of two Similar figures

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M K L J SR Q P Z Quadrilateral JKLM is similar to quadrilateral PQRS. Find the value of Z Example

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Complete Worksheet Assignment

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