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Splash Screen

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Splash Screen Over Lesson 6 1 Lesson Menu Five-Minute Check (over Lesson 6 1) Then/Now New Vocabulary Theorems: Properties of Parallelograms Proof: Theorem 6.4 ... – PowerPoint PPT presentation

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Title: Splash Screen


1
Splash Screen
2
Lesson Menu
Five-Minute Check (over Lesson 61) Then/Now New
Vocabulary Theorems Properties of
Parallelograms Proof Theorem 6.4 Example
1 Real-World Example Use Properties of
Parallelograms Theorems Diagonals of
Parallelograms Example 2 Use Properties of
Parallelograms and Algebra Example
3 Parallelograms and Coordinate Geometry Example
4 Proofs Using the Properties of Parallelograms
3
5-Minute Check 1
Find the measure of an interior angle of a
regular polygon that has 10 sides.
A. 180 B. 162 C. 144 D. 126
  1. A
  2. B
  3. C
  4. D

4
5-Minute Check 2
Find the measure of an interior angle of a
regular polygon that has 12 sides.
A. 135 B. 150 C. 165 D. 180
  1. A
  2. B
  3. C
  4. D

5
5-Minute Check 3
What is the sum of the measures of the interior
angles of a 20-gon?
A. 3600 B. 3420 C. 3240 D. 3060
  1. A
  2. B
  3. C
  4. D

6
5-Minute Check 4
What is the sum of the measures of the interior
angles of a 16-gon?
A. 3060 B. 2880 C. 2700 D. 2520
  1. A
  2. B
  3. C
  4. D

7
5-Minute Check 5
Find x if QRSTU is a regular pentagon.
A. 21 B. 15.25 C. 12 D. 10
  1. A
  2. B
  3. C
  4. D

8
5-Minute Check 6
What type of regular polygon has interior angles
with a measure of 135?
A. pentagon B. hexagon C. octagon D. decagon
  1. A
  2. B
  3. C
  4. D

9
Then/Now
You classified polygons with four sides as
quadrilaterals. (Lesson 16)
  • Recognize and apply properties of the sides and
    angles of parallelograms.
  • Recognize and apply properties of the diagonals
    of parallelograms.

10
Vocabulary
  • parallelogram

11
Concept 1
12
Concept 2
13
Example 1A
Use Properties of Parallelograms
14
Example 1
Use Properties of Parallelograms
15 Substitution
Answer AD 15 inches
15
Example 1B
Use Properties of Parallelograms
16
Example 1
Use Properties of Parallelograms
m?C 32 180 Substitution m?C 148
Subtract 32 from each side.
Answer m?C 148
17
Example 1C
Use Properties of Parallelograms
18
Example 1
Use Properties of Parallelograms
32 Substitution
Answer m?D 32
19
Example 1A
A. ABCD is a parallelogram. Find AB.
A. 10 B. 20 C. 30 D. 50
  1. A
  2. B
  3. C
  4. D

20
Example 1B
B. ABCD is a parallelogram. Find m?C.
A. 36 B. 54 C. 144 D. 154
  1. A
  2. B
  3. C
  4. D

21
Example 1C
C. ABCD is a parallelogram. Find m?D.
A. 36 B. 54 C. 144 D. 154
  1. A
  2. B
  3. C
  4. D

22
Concept 3
23
Example 2A
Use Properties of Parallelograms and Algebra
A. If WXYZ is a parallelogram, find the value of
r.
Opposite sides of a parallelogram are ?.
Definition of congruence
Substitution
Divide each side by 4.
Answer r 4.5
24
Example 2B
Use Properties of Parallelograms and Algebra
B. If WXYZ is a parallelogram, find the value of
s.
s 3 Subtract 7s from each side.
Answer s 3
25
Example 2C
Use Properties of Parallelograms and Algebra
C. If WXYZ is a parallelogram, find the value of
t.
?WXY? ?YZW Diagonal separates a
parallelogram into 2 ?
triangles. ?YWX? ?WYZ CPCTC m?YWX m?WYZ
Def of congruence
2t 18 Substitution t9 Divide each side by 2.
26
Example 2A
A. If ABCD is a parallelogram, find the value of
x.
A. 2 B. 3 C. 5 D. 7
  1. A
  2. B
  3. C
  4. D

27
Example 2B
B. If ABCD is a parallelogram, find the value of
p.
A. 4 B. 8 C. 10 D. 11
  1. A
  2. B
  3. C
  4. D

28
Example 2C
C. If ABCD is a parallelogram, find the value of
k.
A. 4 B. 5 C. 6 D. 7
  1. A
  2. B
  3. C
  4. D

29
Example 3
Parallelograms and Coordinate Geometry
What are the coordinates of the intersection of
the diagonals of parallelogram MNPR, with
vertices M(3, 0), N(1, 3), P(5, 4), and R(3,
1)?
30
Example 3
Parallelograms and Coordinate Geometry
Answer The coordinates of the intersection of
the diagonals of parallelogram MNPR are (1, 2).
31
Example 3
What are the coordinates of the intersection of
the diagonals of parallelogram LMNO, with
vertices L(0, 3), M(2, 1), N(1, 5), O(3, 1)?
  1. A
  2. B
  3. C
  4. D

32
Example 4
To complete the proof below, which of the
following is relevant information?
Prove ?LNO ? ?NLM
  1. A
  2. B
  3. C
  4. D

33
End of the Lesson
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