Corresponding Parts of Geometric Figures

Naming Figures 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 & Comparing Polygons D C B E 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. DCBAE P I J K H D corresponds to  I AE corresponds to PH IJKPH

Name corresponding parts Name all the angles that correspond: P I J K H A D C B E  D corresponds to  I  C corresponds to  J  B corresponds to  K  A corresponds to  P  E corresponds to  H DCBAE IJKPH Name all the segments that correspond: How many corresponding sides are there? 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? 5 5

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

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.

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. C D B A G H F E CONGRUENCE STATEMENT ABCD = EFGH ~

Examples

Helpful Hint When you write a statement such as ABC  DEF, you are also stating which parts are congruent.

Naming Congruent corresponding Parts Given: ∆PQR  ∆STW Identify all pairs of corresponding congruent parts. Angles: P  __, Q  __, R  __ S T W Sides: PQ  __, QR  __, PR  __ ST TW SW

More Practice 1. ∆ABC  ∆JKL and AB = 2x + 12. 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 E ED D DC C EC

Similar Polygons 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.

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

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

Writing Proportions using Corresponding Parts 30 16 B C 10 D E

What is the scale factor? 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. Q 6 R X 4 Y 10 15 W B P S What is the scale factor?

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

Example 10 K J Q Z P 15 6 M L R S Quadrilateral JKLM is similar to quadrilateral PQRS. Find the value of Z

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