Download Lesson 14: Congruent Figures

NYS COMMON CORE MATHEMATICS CURRICULUM
Name:__________________________________
Lesson 14
M1
Period:________ Date:__________
GEOMETRY
Lesson 14: Congruent Figures - Triangles
Learning Target: I can list pairs of corresponding angles and sides on congruent triangles
Things that we should know ……
The word "congruent" is defined in the dictionary as “identical” in form
Congruent figures are the same size and shape. It is possible to turn, flip and/or slide one figure so it will fit
exactly on the other figure.

The areas of congruent figures are equal. The perimeters of congruent figures are equal.

The corresponding angles of congruent figures are equal in measure.

The corresponding line segments of congruent figures are equal in length
These triangles are ≅
These two figures are not ≅
For congruent (≅) triangles, all the angles are congruent AND all the corresponding sides are congruent.
Naming Congruent Triangles
The naming of congruent triangles is important: order matters.
The statement: ΔABC is congruent to ΔDEF indicates that these triangles are congruent.
Therefor all corresponding angles and sides are congruent
Angle measures are equal:
𝑚∠𝐴 = 𝑚∠𝐷
𝑚∠𝐵 = 𝑚∠𝐸
𝑚∠𝐶 = 𝑚∠𝐹
Lengths are equal:
𝐴𝐵 = 𝐷𝐸
𝐵𝐶 = 𝐸𝐹
𝐶𝐴 = 𝐹𝐷
Draw the triangles
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:__________________________________
Lesson 14
Period:________ Date:__________
Identifying Corresponding Parts
Example 1. Given that 𝛥𝐴𝐵𝐶 is congruent to 𝛥𝐷𝐸𝐹, identify all the congruent corresponding parts
a. three pairs of congruent sides
b. three pairs of congruent angles
c. Given that 𝛥𝐴𝐵𝐶 is congruent to 𝛥𝐷𝐸𝐹, mark these triangles accordingly.
Example 2
Example 3
Given that 𝛥𝐴𝐵𝐶 ≅ 𝛥𝐿𝑀𝑁, identify all the corresponding angles and sides.
Corresponding Sides
Corresponding Angles
Draw a diagram
M1
GEOMETRY

NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 14
Name:__________________________________
M1
GEOMETRY
Period:________ Date:__________
Lesson 14: Congruent Figures - Triangles
Classwork
1. Given that  ABC   XYZ, identify and mark all of the congruent corresponding parts in the diagram.
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2.  CAT
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  JSD. List each of the following.
a. three pairs of congruent sides
b. three pairs of congruent angles

For exercises 3 – 5 list the corresponding sides and angles.
3.
Pairs of ≅
angles (#3)
4.
Pairs of ≅
sides (#3)
5.
Pairs of ≅
angles (#4)
Pairs of ≅
sides (#4)
Pairs of ≅
angles (#5)
Write a triangle congruence statement for each pair of triangles above
3.___________________
4.___________________
5.________________
Pairs of ≅
sides (#5)
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 14
M1
GEOMETRY
Name:__________________________________
Period:________ Date:__________
6. If  ACB   JKL, which of the following must be a correct congruence statement?



A. A  L
C. AB  JL
B. B  K
D. BAC  LKJ
7. Given that  DEF   JKL, mark all of the congruent corresponding parts in the
diagram and then list them.
D

E
8.  BAT
J

F
L
K
  COM. List each of the following.
a. three pairs of congruent sides
b. three pairs of congruent angles

For exercises 9 – 11 list the corresponding sides and angles. Write a congruence statement.
9.
Pairs of ≅
angles (#9)
10.
Pairs of ≅
sides (#9)
11.
Pairs of ≅
angles (#10)
Pairs of ≅
sides (#10)
Pairs of ≅
angles (#11)
Write a triangle congruence statement for each pair of triangles above
9._________________
10._________________
11.___________________
Pairs of ≅
sides (#11)