Geometry -~~- ~--~-.- "> \) N '" '" -' 16 Objective Identify corresponding parts of congruent figures. Skills • Identifying attributes • Comparing • Reasoning NCTM Expectations Grades 6-8 Geometry • Preciselydescribe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties. • Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship. • Describe sizes,positions, and orientations of shapes under informal transformations such asflips, turns, slides, and scaling. • Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such asart, science,and everyday life. Corresponding Parts of Congruent Figures Corresponding parts of congruent figures match exactly and have equal measures. Recognizing these relationships in triangles allows students to informally explore side and angle relationships used in geometric proofs. It also prepares students to identify congruent angles in similar figures and to use proportionality to find the side lengths in similar figures. lrylt! Perform the TryIt! activity on the next page. ~~l§#~~ !'(¥£'s€~:!€i$$; Talk About It Discussthe Try It! activity. • Ask: How can you identify corresponding parts in congruent triangles when the triangles are in different positions? • Draw two congruent isoscelestriangles on the board. Have students identify corresponding sides and corresponding angles. • Discussthat corresponding sidesand angles in congruent figures always have the same measure. Solve It Reread the problem with students. Have students draw two congruent frames and use different colors to mark the pairs of corresponding sides and corresponding angles in the two figures. Ask them to explain how Joshua can use corresponding parts to make sure the frames are congruent. More Ideas For other ways to teach about corresponding parts of congruent figures- • Usegeoboards to make congruent figures. Have students use same- color bands to show corresponding sides.They can visually compare corresponding angles by referring to the color of the segments making up the angles. • Have students use Anql.eqs" to model congruency in different polygons. Standardized Practice Have students try the following problem. Which is a pair of corresponding parts in these congruent triangles? A. LA and LB B E B. LD and LB A~C / c. AC and DF D. CBand DE D

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Page 1: N Corresponding Parts of Congruent Figures

Geometry

-~~- ~--~-.-

"> \) N'"'"-' 16

ObjectiveIdentify corresponding parts ofcongruent figures.

Skills• Identifying attributes• Comparing• Reasoning

NCTMExpectationsGrades 6-8Geometry• Precisely describe, classify,and understand relationshipsamong types of two- andthree-dimensional objectsusing their definingproperties.

• Create and critique inductiveand deductive argumentsconcerning geometric ideasand relationships, suchas congruence, similarity,and the Pythagoreanrelationship.

• Describe sizes, positions, andorientations of shapes underinformal transformationssuch as flips, turns, slides,and scaling.

• Recognize and applygeometric ideas andrelationships in areas outsidethe mathematics classroom,such as art, science, andeveryday life.

Corresponding Parts ofCongruent FiguresCorresponding parts of congruent figures match exactly and have equalmeasures. Recognizing these relationships in triangles allows students toinformally explore side and angle relationships used in geometric proofs. Italso prepares students to identify congruent angles in similar figures and touse proportionality to find the side lengths in similar figures.

lrylt! Perform the TryIt! activity on the next page.

~~l§#~~ !'(¥£'s€~:!€i$$;

Talk About ItDiscussthe Try It! activity.

• Ask: How can you identify corresponding parts in congruent triangles whenthe triangles are in different positions?

• Draw two congruent isoscelestriangles on the board. Have students identifycorresponding sides and corresponding angles.

• Discussthat corresponding sides and angles in congruent figures alwayshave the same measure.

Solve ItReread the problem with students. Have students draw two congruentframes and use different colors to mark the pairs of corresponding sides andcorresponding angles in the two figures. Ask them to explain how Joshua canuse corresponding parts to make sure the frames are congruent.

More IdeasFor other ways to teach about corresponding parts of congruent figures-

• Use geoboards to make congruent figures. Have students use same-color bands to show corresponding sides. They can visually comparecorresponding angles by referring to the color of the segments makingup the angles.

• Have students useAnql.eqs" to model congruency in different polygons.

Standardized PracticeHave students try the following problem.

Which is a pair of corresponding parts in these congruent triangles?

A. LA and LB B EB. LD and LB

A~C /c. AC and DF

D. CBand DE D