65 rhombi and squares - pc\|macimages.pcmac.org/sisfiles/schools/al/dalevillecs/... · 2019. 9....
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Geo 65 Lesson with notes 3rd b.notebook
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February 16, 2016
Nov 29:52 AM
65 Rhombi and Squares
Learning Targets:I can recognize and apply the properties of rhombi and squaresI can determine whether quadrilaterals are rectangles, rhombi, or
squares
Why can a rhombus and a square also be classified as equilateral parallelograms?
In what ways can you classify rhombi and squares?
Is it possible for a rhombus to have exactly one 90 angle? Exactly two? Explain your reasoning.
Feb 311:29 AM
Geo 65 Lesson with notes 3rd b.notebook
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February 16, 2016
Feb 311:42 AM
Feb 311:53 AM
Geo 65 Lesson with notes 3rd b.notebook
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February 16, 2016
Feb 311:56 AM
Jan 228:59 PM
Rhombus: a parallelogram with all four sides congruent.
It has all the properties of parallelograms and two additional ones.
Geo 65 Lesson with notes 3rd b.notebook
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February 16, 2016
Jan 229:07 PM
Jan 229:08 PM
Geo 65 Lesson with notes 3rd b.notebook
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February 16, 2016
Jan 229:09 PM
Example 1:
The diagonals of a rhombus WXYZ intersect at V. Use the given information to find each measure or value.
1. If m<WZX = 39.5, find m<ZYX.
2. If WX = 8x 5 and WZ = 6x + 3, find x.
Jan 229:12 PM
Refer to the rhombus FGHJ.
3. If FK = 5 and FG = 13, find KJ.
4. If m<JFK = 6y + 7 and m<KFG = 9y 5, find y.
Geo 65 Lesson with notes 3rd b.notebook
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February 16, 2016
Jan 236:18 AM
Square: a parallelogram with four congruent sides and four right angles.
Recall, a rectangle is a parallelogram with four right angles and a rhombus is a parallelogram with four congruent sides, therefore, a square is both a rectangle and a rhombus.
Jan 236:22 AM
All properties of parallelograms, rectangles, and rhombi apply to squares.
For example: the diagonals of a square bisect each other (parallelogram), are congruent (rectange), and are perpendicular (rhombus).
Geo 65 Lesson with notes 3rd b.notebook
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February 16, 2016
Jan 236:25 AM
Jan 236:27 AM
Geo 65 Lesson with notes 3rd b.notebook
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February 16, 2016
Jan 236:28 AM
Example 2:
5. Write a twocolumn proof.
Given: LMNP is a parallelogram, <1 ≅ <2 and <2 ≅ <6.
Prove: LMNP is a rhombus.
Jan 236:36 AM
6. Write a twocolumn proof.
Given: SQ is the perpendicular bisector of PR. PR is the perpendicular bisector of SQ. ΔRMS is isosceles.
Prove: PQRS is a square.
Geo 65 Lesson with notes 3rd b.notebook
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February 16, 2016
Jan 236:39 AM
Jan 236:44 AM
Example 3:
7. Hector is measuring the boundary of a new garden. He wants the garden to be square. He has set each of the corner stakes 6 feet apart. What does Hector need to know to make sure that the garden is a square?
Geo 65 Lesson with notes 3rd b.notebook
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February 16, 2016
Jan 236:47 AM
8. Kathy is designing a quilt with blocks like the one shown.
a) If she marks the diagonals of each yellow piece and determines that each pair of diagonals is perpendicular, can she conclude that each yellow piece is a rhombus? Explain.
b) If all four angles of the green piece have the same measure and the botom and left sides have the same measure, can she conclude that the green piece is a square? Explain.
Jan 236:52 AM
Geo 65 Lesson with notes 3rd b.notebook
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February 16, 2016
Jan 236:55 AM
Example 4:
9. Determine whether parallelogram ABCD is a rhombus, a rectangle, or a square for A(2, 1), B(1, 3), C(3, 2), and D(2, 2). List all that apply. Explain.