Corresponding Sides - Geometry

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Position Sides

Corresponding Sides
Definition of Corresponding Sides

If the relative position of two sides is same in two figures, then they are called Corresponding Sides.

More about Corresponding Sides

Corresponding sides are proportional in similar figures.

Example of Corresponding Sides

In the figure, triangles ABC and XYZ are similar.
The relative position of AB and XY is same, so they are corresponding sides.
Similarly, BC and YZ, and AC and XZ, are corresponding sides.

Solved Example on Corresponding Sides

If the pentagons shown are similar, identify the corresponding sides.

Choices:
A. and
B. and
C. and
D. and
Correct Answer: A
Solution:
Step 1: Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.
Step 2: So, PQ/AB = QR/BC = RT/CD = TS/DE = SP/EA [Proportion of sides.]
Step 3: Here, and are corresponding sides.

Related Terms for Corresponding Sides

Position
Sides

Additional Links for Corresponding Sides

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Browse for solved examples below on this Math Dictionary term:

PA BM Curriculum > Grade 7 > Geometry > 7.C.1.2.2: Identify corresponding sides and/or angles of similar polygons

Michigan Assessment Curriculum - 2006 > Benchmark - Algebra II > Interpreting Geometry > G.GS.06.02-Understand that for polygons, congruence means corresponding sides and angles have equal measures.

Michigan Assessment Curriculum - 2006 > Grade 6 > Interpreting Geometry > G.GS.06.02-Understand that for polygons, congruence means corresponding sides and angles have equal measures.

Michigan Assessment Curriculum - 2006 > Grade 7 > Interpreting Geometry > G.TR.07.03-Understand that in similar polygons, corresponding angles are congruent and the ratios of corresponding sides are equal; understand the concepts of similar figures and scale factor.

Michigan Assessment Curriculum - 2006 > Grade 7 > Interpreting Geometry > G.TR.07.05-Show that two triangles are similar using the criteria: corresponding angles are congruent (AAA similarity); the ratios of two pairs of corresponding sides are equal and the included angles are congruent (SAS similarity); ratios of all pairs of corresponding sides are equal (SSS similarity); use these criteria to solve problems and to justify arguments.

Missouri Assessment Curriculum - 2006 > Benchmark - Algebra II > Geometry > G.1.B.6.ai-Describe relationships between the corresponding angles and the length of corresponding sides of similar triangles (whole number scale factors).

Missouri Assessment Curriculum - 2006 > Grade 6 > Geometry > G.1.B.6.ai-Describe relationships between the corresponding angles and the length of corresponding sides of similar triangles (whole number scale factors).

Missouri Assessment Curriculum - 2006 > Grade 7 > Geometry > G.1.B.7.ai-Describe relationships between corresponding sides, corresponding angles and corresponding perimeters of similar polygons.

Missouri Assessment Curriculum - 2006 > Grade 8 > Geometry > G.1.B.8.ai-Apply relationships between corresponding sides and corresponding areas of similar polygons to solve problems.

Ohio Assessment Curriculum - 2006 > Benchmark - Algebra II > Geometry > 6-Draw similar figures that model proportional relationships; e.g., model similar figures with a 1 to 2 relationship by sketching two of the same figure, one with corresponding sides twice the length of the other.

Ohio Assessment Curriculum - 2006 > Grade 6 > Geometry > 6-Draw similar figures that model proportional relationships; e.g., model similar figures with a 1 to 2 relationship by sketching two of the same figure, one with corresponding sides twice the length of the other.

Ohio Assessment Curriculum - 2006 > Grade 8 > Geometry > 3-Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures).

Oregon Assessment Curriculum - 2006 > Grade 5 > Interpreting Geometry > MA.05.GM.04-Draw conclusions about the measures of corresponding sides and angles of two congruent and similar triangles.

Oregon Assessment Curriculum - 2006 > Grade 8 > Interpreting Geometry > MA.08.GM.03-Determine the measures of corresponding sides and angles of congruent and similar triangles and their component parts.

New York Assessment Curriculum - 2006 > Grade 5 > Interpreting Geometry > 5.G.3-Identify the ratio of corresponding sides of similar triangles.

New York Assessment Curriculum - 2006 > Benchmark - Algebra II > Interpreting Geometry > 6.G.1-Calculate the length of corresponding sides of similar triangles, using proportional reasoning.

New York Assessment Curriculum - 2006 > Grade 6 > Interpreting Geometry > 6.G.1-Calculate the length of corresponding sides of similar triangles, using proportional reasoning.

Kansas Assessment Curriculum - 2006 > Algebra - 1 > Geometric Figures and Their Properties – The student recognizes geometric figures and compares and justifies their properties of geometric figures in a variety of situations. > 3.1.4-The student recognizes that similar figures have congruent angles, and their corresponding sides are proportional.

Kansas Assessment Curriculum - 2006 > Geometry > Geometric Figures and Their Properties – The student recognizes geometric figures and compares and justifies their properties of geometric figures in a variety of situations. > 3.1.4-The student recognizes that similar figures have congruent angles, and their corresponding sides are proportional.

Pennsylvania Assessment Curriculum - 2006 > Grade 7 > Interpreting Geometry > 7.C.1.2.2-Identify corresponding sides and/or angles of similar polygons.

Georgia Assessment Curriculum - 2006 > Grade 8 > M8G1 Students will understand and apply the properties of parallel and perpendicular lines and understand the meaning of congruence. > M8G1.d-Understand the meaning of congruence: that all corresponding angles are congruent and all corresponding sides are congruent.

NCERT Assessment Curriculum 2007 > > Triangles > (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.

NCERT Assessment Curriculum - 2007 > Geometry > TRIANGLES > (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.

NCERT Assessment Curriculum - 2007 > Geometry > TRIANGLES > (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.

NCERT Assessment Curriculum - 2007 > Geometry > TRIANGLES > (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.

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