Download 10.1 Notes and HW Quads and Parallelograms.pages

Name: ________________________________
Unit 10: Quadrilaterals
5/18/15
Geo – Pilch
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And now for something completely different...QUADRILATERALS!
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TRUE FACTS ABOUT QUADRILATERALS:
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Quadrilaterals are always named by: __________________________________________________.
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Example 1:
This quadrilateral could be named ____________ or _____________ or _____________
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But NOT ______________.
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List all four pairs of consecutive angles: _________, _________, _________, _________
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Name its diagonals: ____________ ______________
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TRUE FACTS ABOUT PARALLELOGRAMS:
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(Label these on the diagrams at right as well ➜ )
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• Opposite sides are parallel
• Opposite sides are congruent
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• Opposite angles are congruent
• Diagonals bisect each other
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• Consecutive angles are supplementary
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Example 2:
Find the measure of ∠B in quadrilateral ABCD if m∠A = x , m∠B = 2x, m∠C = x −10, and m∠D = 50 .
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Example 3:
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In parallelogram PQRS, PQ = 20, QR = 15, and m∠S = 70° .
Find the measure of all sides and angles.
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Example 4:
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In !DEFG, DE = 70, EF = 45, m∠G = 68°. Find:
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a) GF
b) DG
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c) m∠E
d) m∠F
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Example 4.5: In Example 4 above, if point H is the intersection
point of DF and EG, and DF = 40, how long is DH?
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Example 5:
Given:
ABCD is a parallelogram.
m∠1 = 13x +18
m∠2 = 11x + 6
m∠3 = 23x − 22
m∠4 = 50
(a) List all pairs of || sides, and mark them on the diagram.
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(b)Find m∠1 .
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A
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Name: ________________________________
Unit 10: Quadrilaterals
5/18/15
Geo – Pilch
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Homework #1 – Some Perfectly Pleasant Parallelogram Practice
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1. In quadrilateral QRST, at right:
a. Name a consecutive side to RS. ____________________
b. Name the side opposite ST. _______________________
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c. Name a pair of consecutive vertices. ___________________
d. Name the vertex opposite S. _______________________
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e. Name the two diagonals. ________________________
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f. Name a pair of consecutive angles. ____________________
2. In quadrilateral BCDA, find the measure of angle A if
m∠B = 60°, m∠C = 2x + 5, and m∠D = x, and , m∠A = 2x + 5 .
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m∠A = __________________
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3. Find the missing angle measures in each figure:
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(a)
(b)
(c)
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Of (a), (b), and (c), which MUST be parallelograms? JUSTIFY your answer!!
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4. Draw parallelogram MEND with diagonals MN and DE intersecting at point x. Name four pairs of
congruent segments.
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5. If one angle in a parallelogram measures 50°, what are the measures of the other three angles?
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9. In a parallelogram, the measure of one angle is twice that of another angle. Find the measure of all four
angles in the parallelogram. (Draw a picture if you are stuck.)
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10. TRUE or FALSE?
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a. The diagonals of a parallelogram are congruent.
b. When one diagonal is drawn in a parallelogram, it forms two congruent triangles.
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c. If you know the length of one side in a parallelogram, you can find the lengths of the other three sides.
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Perimeter: __________________
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CHALLENGE!!
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Perimeter: __________________