Geometry: Rhombuses, Rectangles, and Squares, High school final essays of Geometry

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Geometry: Unit 8 Lesson 4

Rhombuses,

Rectangles, and

Squares

Warm-Up • Guided Notes •

In-Class Practice • Homework

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Teacher Notes Unit 8 Lesson 4 Rhombi, Rectangles, and Squares

• This lesson includes a warm-up, guided notes, in-class practice, and homework. Answer keys are included.
• Two levels of guided notes are included. One version has more information filled in for the students. You are free to choose whichever is appropriate for your students.
• The guided notes can be inserted into SMART board software or projected onto a whiteboard so that students can follow along.
• The in-class practice includes material from properties of parallelograms as well as rhombi, rectangles, and squares. Mistakes happen! Please forgive me if you find a mistake or typo. Contact me at [email protected] and I will do my best to correct the error as soon as possible. ©2015 Mrs. E Teaches Math This is a lesson from Unit 8 - Polygons and Quadrilaterals in my Geometry curriculum.

Geometry Name _____________

8.4 Warm-Up

A quadrilateral is a parallelogram if…

1. ___________________________________________

___________________________________________

2. ___________________________________________

___________________________________________

3. ___________________________________________

___________________________________________

4. ___________________________________________

___________________________________________

5. ___________________________________________

___________________________________________

©2015 Mrs. E Teaches Math ©2015 Mrs. E Teaches Math

Geometry Name _____________

8.4 Warm-Up

A quadrilateral is a parallelogram if…

1. ___________________________________________

___________________________________________

2. ___________________________________________

___________________________________________

3. ___________________________________________

___________________________________________

4. ___________________________________________

___________________________________________

5. ___________________________________________

___________________________________________

©2015 Mrs. E Teaches Math 8 .4 Rhombi, Rectangles, and Squares Notes Reminders!

• The sum of the measures of the interior angles of a quadrilateral is 360 o.
• A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
• The opposite sides of a parallelogram are congruent.
• The opposite angles of a parallelogram are congruent.
• The consecutive angles of a parallelogram are supplementary.
• The diagonals of a parallelogram bisect each other. Definition: A rhombus is a quadrilateral with four congruent sides. (plural: rhombi or rhombuses) Properties of Rhombi The sides of a rhombus are congruent. The diagonals of a rhombus are perpendicular. The diagonals of a rhombus bisect opposite angles. Notes: The diagonals of a rhombus form four right triangles. Examples
• HOME is a rhombus. Find the values of a , b , and c.
• Find the measures of the numbered angles in the rhombus. Definition: A rectangle is a quadrilateral with four right angles. D B C A E A B C D E A B C D c b a 3 E^4 M O H 54 ° 2 3 4 1

8.4 Rhombi, Rectangles, and Squares Notes ©2015 Mrs. E Teaches Math Properties of Rectangles A rectangle has four right angles. The diagonals of a rectangle are congruent. Note: The diagonals of a rectangle form four isosceles triangles. The two angles formed at each vertex are complementary. Examples

• ABCD is a rectangle. Find AC. • Find the measures of the numbered angles in the rectangle. Definition: A square is a quadrilateral with four right angles and four congruent sides. Properties of Squares A square is both a rhombus and a rectangle. Examples
• SQRE is a square. Find m ∠ SQE. • Find the value of x in the square. A B D C D C A B 10 E A B D C 4 1 2 3 56 ° E A (^) B D C E R S Q 4 x 12

©2015 Mrs. E Teaches Math 8 .4 Rhombi, Rectangles, and Squares Notes Reminders!

• The sum of the measures of the interior angles of a quadrilateral is ________.
• A parallelogram is a quadrilateral with both pairs of opposite sides ____________.
• The opposite sides of a parallelogram are _______________.
• The opposite angles of a parallelogram are ________________.
• The consecutive angles of a parallelogram are __________________.
• The diagonals of a parallelogram ____________ each other. Definition: A rhombus is a quadrilateral with four ________________ sides. (plural: rhombi or rhombuses) Properties of Rhombi The sides of a rhombus are _______________. The diagonals of a rhombus are _________________. The diagonals of a rhombus ___________ opposite angles. Notes: The diagonals of a rhombus form _____________ _____________ _____________. Examples
• HOME is a rhombus. Find the values of a , b , and c.
• Find the measures of the numbered angles in the rhombus. Definition: A rectangle is a quadrilateral with four _____________ angles. D B C A E A B C D E A B C D c b a 3 E^4 M O H 54 ° 2 3 4 1

8.4 Rhombi, Rectangles, and Squares Notes ©2015 Mrs. E Teaches Math Properties of Rectangles A rectangle has four __________ angles. The diagonals of a rectangle are _______________. Note: The diagonals of a rectangle form four _____________ triangles. The two angles formed at each vertex are _______________. Examples

• ABCD is a rectangle. Find AC. • Find the measures of the numbered angles in the rectangle. Definition: A square is a quadrilateral with four ___________ angles and four _______________ sides. Properties of Squares A square is both a rhombus and a rectangle. Examples
• SQRE is a square. Find m ∠ SQE. • Find the value of x in the square. A B D C D C A B 10 E A B D C 4 1 2 3 56 ° E A (^) B D C E R S Q 4 x 12

©2015 Mrs. E Teaches Math 8 .4 Mixed Review In-Class Practice Name ________________ Date _______ Per _____ Show your work where possible.

1. Find the value of x. 2. Find the value of x and y.
2. Find the value of x. 4. Find the value of x and y.
3. PQRS is a rhombus. The length of the shorter diagonal, PR , is 12 cm and m ∠ PQR = 60 °. Find the length of a side of the rhombus. 6. In rectangle ABCD , diagonals AC and BD meet at point E. If CB = 6 , AB = 8 , and AC = 10 , find the lengths of AD , CD , AE , and DB.
4. Prove that JKLM is a parallelogram by showing that one pair of opposite sides are both parallel and congruent. J (^) (− 6 , (^2) ), K (^) (− 1 , (^3) ), L (^) ( 2 ,− (^3) ), M (^) ( − 3 ,− (^4) ) x + 5 3 x - 11 56 ° y - 60 3 x + 4 16 5 x 4 x 16 6 y - 5 x + 2

©2015 Mrs. E Teaches Math ABCD is a square.

11. If AX = 6 , then BD = _____.
12. m ∠ BXC = _____ , m ∠ ACD = _____ , and m ∠ ABC = _____.
13. If the perimeter of ABCD is 36, then AB = ________.
14. If the perimeter of ABCD is 40, then AC = ________. ABCD is a rhombus.
15. If m ∠ DAB = 130 ° , then m ∠ ADC = _____ , m ∠ 1 = _____ , m ∠ 2 = _____ , m ∠ 3 = _____ , m ∠ 4 = _____ , and m ∠ 5 = _____.
16. If m ∠ 4 = 3 x − 2 and m ∠ 5 = 2 x + 7 , then x = _____ , m ∠ 2 = _____ , and m ∠ 4 = _____.
17. If m ∠ 2 = 3 y + 9 and m ∠ 4 = 2 y − 4 , then y = _____ , m ∠ 2 = _____ , m ∠ 4 = _____ , and m ∠ 5 = _____.

D C

A B

X

1 2 4 3 A 5 D C B