Transcript B - Spring Branch ISD

LESSON 6–3
Tests for Parallelograms
Five-Minute Check (over Lesson 6–2)
TEKS
Then/Now
Theorems: Conditions for Parallelograms
Proof: Theorem 6.9
Example 1: Identify Parallelograms
Example 2: Real-World Example: Use Parallelograms to Prove
Relationships
Example 3: Use Parallelograms and Algebra to Find Values
Concept Summary: Prove that a Quadrilateral Is a
Parallelogram
Example 4: Parallelograms and Coordinate Geometry
Example 5: Parallelograms and Coordinate Proofs
Over Lesson 6–2
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____
A.
B.
C.
Over Lesson 6–2
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A.
B.
C.
Over Lesson 6–2
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A. A
B. B
C. C
Over Lesson 6–2
An expandable gate is made of parallelograms that
have angles that change
measure as the gate is
adjusted. Which of the
following statements is
always true?
A. A  C and B  D
B. A  B and C  D
C.
D.
Targeted TEKS
G.6(E) Prove a quadrilateral is a parallelogram, rectangle,
square, or rhombus using opposite sides, opposite angles, or
diagonals and apply these relationships to solve problems.
Mathematical Processes
G.1(D), G.1(G)
You recognized and applied properties of
parallelograms.
• Recognize the conditions that ensure a
quadrilateral is a parallelogram.
• Prove that a set of points forms a
parallelogram in the coordinate plane.
Identify Parallelograms
Determine whether the quadrilateral is a
parallelogram. Justify your answer.
Answer: Each pair of opposite sides has the same
measure. Therefore, they are congruent.
If both pairs of opposite sides of a
quadrilateral are congruent, the quadrilateral
is a parallelogram.
Which method would prove the
quadrilateral is a parallelogram?
A. Both pairs of opp. sides ||.
B. Both pairs of opp. sides .
C. Both pairs of opp. s .
D. One pair of opp. sides both
|| and .
The diagram shows a car jack used to raise a car
from the ground. In the diagram, AD  BC and
AB  DC. Based on this information, which
statement will be true, regardless of the height of
the car jack.
A. A  B
B. A  C
C. AB  BC
D. mA + mC = 180
Use Parallelograms and Algebra to Find Values
Find x and y so that the quadrilateral is a
parallelogram.
Opposite sides of a parallelogram are congruent.
Use Parallelograms and Algebra to Find Values
AB = DC
Substitution
Distributive Property
Subtract 3x from each side.
Add 1 to each side.
Use Parallelograms and Algebra to Find Values
Substitution
Distributive Property
Subtract 3y from each side.
Add 2 to each side.
Answer: So, when x = 7 and y = 5, quadrilateral
ABCD is a parallelogram.
Find m so that the quadrilateral is a parallelogram.
A. m = 2
B. m = 3
C. m = 6
D. m = 8
LESSON 6–3
Tests for Parallelograms