(8) Lesson 7.2 - Congruence

1. Course 3, Lesson 7-2
Determine if the two figures are congruent by using
transformations. Explain your reasoning.
1. 2.
3. Triangle ABC is congruent to triangle XYZ. Give a series of
transformations that maps triangle XYZ onto triangle ABC.

2. Course 3, Lesson 7-2
ANSWERS
1. congruent; rotation 90° clockwise and then a translation
2. congruent; rotation 90° counterclockwise and then a translation
3. reflection then translation

3. HOW can you determine
congruence and similarity?
Geometry
Course 3, Lesson 7-2

4. Course 3, Lesson 7-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council
of Chief State School Officers. All rights reserved.
• 8.G.2
Understand that a two-dimensional figure is congruent to another if
the second can be obtained from the first by a sequence of
rotations, reflections, and translations; given two congruent figures,
describe a sequence that exhibits the congruence between them.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Geometry

5. To
• compare corresponding parts of
congruent figures,
• find missing measures of angles
and sides of congruent figures
Course 3, Lesson 7-2
Geometry

6. • corresponding parts
Symbols
• is congruent to
Course 3, Lesson 7-2

Geometry

7. Course 3, Lesson 7-2
Geometry
Words If two figures are congruent, their corresponding sides are
congruent and their corresponding angles are congruent.
Model
Symbols
Congruent Angles:
Congruent Sides:
ABC DEF
; ;A D B E C F     
; ;AB DE BC EF CA FD  

8. 1
Need Another Example?
2
3
Step-by-Step Example
1. Write congruence statements
comparing the corresponding parts
in the congruent triangles shown.
Use the matching arcs and tick marks to identify
the corresponding parts.
Corresponding angles: ∠J ∠G, ∠L ∠I, ∠K ∠H
Corresponding sides: JK GH, KL HI, LJ IG

9. Answer
Need Another Example?
Write congruence statements comparing the
corresponding parts in the congruent triangles
shown.
∠P ∠C, ∠Q ∠B, ∠R ∠D,
RQ DB; RP DC; PQ CB

10. Determine any changes in the orientation of the triangles. The orientation is
reversed so at least one of the transformations is a reflection. If you reflect
ABC over the y-axis and then translate it down 2 units it coincides with XYZ.
1
Need Another Example?
2
3
Step-by-Step Example
2. Triangle ABC is
congruent to XYZ.
Write congruence
statements comparing
the corresponding
parts. Then determine
which transformations
map ABC onto XYZ.
The transformations that map ABC onto XYZ consist of a
reflection over the y-axis followed by a translation of 2 units down.
Analyze the figures to determine which angles and sides of the figures correspond.
Corresponding angles: ∠A ∠X, ∠B ∠Y, ∠C ∠Z
Corresponding sides: AB XY, BC YZ, CA ZX

11. Answer
Need Another Example?
Triangle RST is congruent to NML. Write
congruence statements comparing the
corresponding parts. Then determine which
transformation(s) maps RST onto NML.
∠R ∠N, ∠S ∠M, ∠T ∠L,
RS NM; RT NL; ST ML;
Sample answer: If you reflect RST over
the x-axis and then translate it to the left
6 units, it coincides with NML.

12. 1
Need Another Example?
Step-by-Step Example
3. Miley is using a brace to support a tabletop. In the figure, BCE DFG.
If m∠CEB = 50°, what is the measure of ∠FGD?
Since ∠CEB and ∠FGD are corresponding parts in congruent
figures, they are congruent. So, ∠FGD measures 50°.

13. Answer
Need Another Example?
In the figure below, quadrilateral ABCD is congruent to
quadrilateral WXYZ. What is the measure of ∠X?
145°

14. How did what you learned
today help you answer the
HOW can you determine
congruence and similarity?
Course 3, Lesson 7-2
Geometry

15. How did what you learned
today help you answer the
HOW can you determine
congruence and similarity?
Course 3, Lesson 7-2
Geometry
Sample answers:
• Two figures are congruent if their corresponding sides
are congruent and their corresponding angles are
congruent.
• On the coordinate plane, you can use the Distance
Formula to find the lengths of sides of figures to see if
corresponding sides are congruent.

16. What must be true about
the corresponding angles
and corresponding sides
of two polygons for them
to be congruent?
Course 3, Lesson 7-2
Ratios and Proportional RelationshipsFunctionsGeometry