Mathematics
Grade 7
15 min
Identify congruent and similar figures
Identify congruent and similar figures
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1
Introduction & Learning Objectives
Learning Objectives
Define congruent figures and similar figures.
Identify corresponding sides and angles in geometric figures.
Determine if two figures are congruent by comparing their corresponding parts.
Determine if two figures are similar by comparing their corresponding parts and calculating the scale factor.
Distinguish between congruent and similar figures based on their properties.
Apply the concepts of congruence and similarity to solve simple geometric problems.
Have you ever noticed how some objects look exactly the same, while others are the same 'shape' but different 'sizes'? 🤔
In this lesson, you'll learn how to precisely describe these relationships using the mathematical terms 'congruent' and 'similar'. Understa...
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Key Concepts & Vocabulary
TermDefinitionExample
Congruent FiguresTwo figures are congruent if they have the exact same shape and the exact same size. One figure can be placed exactly on top of the other through a series of rigid transformations (translations, rotations, reflections).Two identical squares, each with side lengths of 5 cm, are congruent.
Similar FiguresTwo figures are similar if they have the exact same shape but can be different sizes. One figure can be transformed into the other through a dilation (enlargement or reduction) and/or rigid transformations.A small square with 2 cm sides and a large square with 6 cm sides are similar.
Corresponding PartsThese are the matching sides and angles in two or more figures. If you were to overlay the figures, the corresponding parts would line up.In two similar...
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Core Formulas
Rule for Congruent Figures
Two figures are congruent if and only if all their corresponding angles are equal in measure AND all their corresponding sides are equal in length.
To check for congruence, you must verify that every matching angle has the same degree measure and every matching side has the same length. If even one pair of corresponding parts is different, the figures are not congruent.
Rule for Similar Figures
Two figures are similar if and only if all their corresponding angles are equal in measure AND all their corresponding sides are proportional (meaning they have the same constant ratio, or scale factor).
To check for similarity, first ensure all matching angles are equal. Then, calculate the ratio of corresponding side lengths. If all these ratios are the sa...
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Challenging
In the figure, line segment DE is parallel to line segment BC. Triangle ADE is similar to triangle ABC. If AD = 6, DB = 3, and DE = 8, what is the length of BC?
A.10
B.12
C.4
D.16
Challenging
Triangle A has vertices at (1,1), (4,1), and (1,5). Triangle B has vertices at (2,8), (8,8), and (2,16). What is the relationship between Triangle A and Triangle B?
A.They are congruent.
B.They are neither similar nor congruent.
C.They are similar.
D.They are reflections of each other.
Challenging
A rhombus has all four sides equal. Rhombus 1 has side lengths of 5 and angles of 80° and 100°. Rhombus 2 has side lengths of 10 and angles of 90° and 90° (making it a square). Why are these two figures NOT similar?
A.Their corresponding angles are not equal.
B.Their corresponding sides are not proportional.
C.They are similar, the statement is false.
D.One is a rhombus and one is a square.
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