Similar and Congruent Figures (
)
Math 7
Vocabulary
***Similar Figures: a figure having the same shape
but not necessarily the same size.
***Corresponding Parts: sides or angles that have the
same relative position.
***Congruent: 2 figures that have the same shape
and the same size.
***Properties of Similar Figures
ABC
DEF
1. Corresponding angles of similar
figures are congruent.
A D, B E, C F
2. The ratios of the lengths of
corresponding sides of similar figures
are equal.
Examples
** Ex. 1: Identifying Corresponding Parts of Similar
Figures
Given LMN
PQR, name the corresponding
angles and the corresponding sides.
Corresponding angles:
and R
L and P, M and Q, N
Corresponding sides:
Try these on your own
1. Given ABCD WXYZ , name
the corresponding angles
and the corresponding
sides.
** Ex. 2: Finding the Ratio of Corresponding Side
Lengths
Given ABCD JKLM , find the ratio of the lengths of
corresponding sides of ABCD to JKLM.
Write a ratio comparing the
lengths of a pair of
corresponding sides. Then substitute the lengths of
the sides and simplify.
Try these on your own: Find the ratio
** Ex. 3: Finding Measures of Congruent Figures
Given ABCD WXYZ , find the
indicated measure.
a. WZ
b. m W
Solution a.
So, WZ = AD = 12 m.
b. W
A. So, m W = m A = 105º.
Try these on your own
1. Given RSTU
ABCD, find the
indicated measure.
13. m R
Guided Practice/Ticket out the Door