Download Section 5-2 Congruent Polygons Solutions Gordon

Geometry
PreQuiz 5A
POINTS, LINES AND PLANES
1. Find the value of x and
explain how you know.
A
C
B
2. Find 𝑚∠ACB and
classify ∆𝐴𝐵𝐶 by its
angles and sides.
Geometry
PreQuiz 4E
POINTS, LINES AND PLANES
State whether the transformation appears to be congruent
or similar. Also determine which composition of
transformations occurred. Triangle ABC → _______.
Congruent or similar?
A(-3,4)
A
Transformations:
1.
B(-5,1)
C(-1,3)
C
B
2.
D(3,-1)
E(5,-4)
F(1,-2)
D
F
E
Geometry
POINTS,Polygons
LINES AND PLANES
5-2 Congruent
What is required to show that
two triangles are congruent.
Learning Objective: Students will be able to
identify and use corresponding parts of polygons.
Learning Target 5C I can identify congruent
triangles and use the congruency to find missing
sides and angles.
Geometry
POINTS, LINES
AND PLANES
5- 2 Congruent
Polygons
Page 130
Corresponding Parts – Angles or sides of one polygon that
map each part of a figure after a rigid motion.
Congruent Polygons – Two polygons are congruent iff one
can be mapped to the other through a series of rigid
motion transformations.
If two polygons are congruent then their corresponding
parts are congruent.
Geometry
POINTS, LINES
AND PLANES
5- 2 Congruent
Polygons
Page 130
Example: List the corresponding angles and sides and write a
congruence statement.
Geometry
POINTS, LINES
AND PLANES
5- 2 Congruent
Polygons
Page 130
Geometry
POINTS, LINES
AND PLANES
5- 2 Congruent
Polygons
Page 130
Theorem 5.4 Third Angle Theorem
If two angles of one triangle are congruent to two angles
of another triangle, then the third angles are also
congruent.
Geometry
POINTS, LINES
AND PLANES
5- 2 Congruent
Polygons
Page 131
In Exercises 1 and 2, identify all pairs of congruent
corresponding parts. Then write another congruence
statement for the polygons.
1. ∆𝑃𝑄𝑅 ≅ ∆𝑆𝑇𝑈
Geometry
POINTS, LINES
AND PLANES
5- 2 Congruent
Polygons
Page 131
In Exercises 1 and 2, identify all pairs of congruent
corresponding parts. Then write another congruence
statement for the polygons.
2. ABCD ≅ 𝐸𝐹𝐺𝐻
Geometry
POINTS, LINES
AND PLANES
5- 2 Congruent
Polygons
Page 131
In Exercises 3 and 4, find the value of x and y.
3. ∆𝑋𝑌𝑍 ≅ ∆𝑅𝑆𝑇
Geometry
POINTS, LINES
AND PLANES
5- 2 Congruent
Polygons
Page 131
In Exercises 3 and 4, find the value of x and y.
4. 𝐴𝐵𝐶𝐷 ≅ 𝐸𝐹𝐺𝐻
Geometry
POINTS, LINES
AND PLANES
5- 2 Congruent
Polygons
Page 132
In Exercises 5 and 6, show that the polygons are congruent.
Explain your reasoning. Write a congruence statement as
well.
Geometry
POINTS, LINES
AND PLANES
5- 2 Congruent
Polygons
In Exercises 7 and 8, find 𝑚∠1.
Page 132