1. Lesson 8-4
Rectangles

2. 5-Minute Check on Lesson 8-3
Transparency 8-4
5-Minute Check on Lesson 8-3
Determine whether each quadrilateral is a parallelogram. Justify your answer. 2.
Determine whether the quadrilateral with the given vertices is a parallelogram using the method indicated.
3. A(,), B(,), C(,), D(,) Distance formula
4. R(,), S(,), T(,), U(,) Slope formula
Which set of statements will prove LMNO a parallelogram? L M
Standardized Test Practice: O N
LM // NO and LO  MN
LO // MN and LO  MN A B
LM  LO and ON  MN
LO  MN and LO  ON C D
Click the mouse button or press the Space Bar to display the answers.

3. 5-Minute Check on Lesson 8-3
Transparency 8-4
5-Minute Check on Lesson 8-3
Determine whether each quadrilateral is a parallelogram. Justify your answer. 2.
Determine whether the quadrilateral with the given vertices is a parallelogram using the method indicated.
3. A(,), B(,), C(,), D(,) Distance formula
4. R(,), S(,), T(,), U(,) Slope formula
Which set of statements will prove LMNO a parallelogram?
Yes, diagonal bisect each other
Yes, opposite angles congruent
Yes, opposite sides equal
No, RS not // UT L M
Standardized Test Practice: O N
LM // NO and LO  MN
LO // MN and LO  MN A B
LM  LO and ON  MN
LO  MN and LO  ON C D
Click the mouse button or press the Space Bar to display the answers.

4. Objectives Recognize and apply properties of rectangles
A rectangle is a quadrilateral with four right angles and congruent diagonals
Determine whether parallelograms are rectangles
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle

5. Vocabulary
Rectangle – quadrilateral with four right angles.

6. Polygon Hierarchy Polygons Quadrilaterals Parallelograms Kites
Trapezoids
Isosceles Trapezoids
Rectangles
Rhombi
Squares

7. The diagonals of a rectangle are congruent, so
Quadrilateral RSTU is a rectangle. If RT = 6x + 4 and SU = 7x - 4 find x.
The diagonals of a rectangle are
congruent, so
Definition of congruent segments
Substitution
Subtract 6x from each side.
Add 4 to each side.
Answer: 8
Example 4-1a

8. Quadrilateral EFGH is a rectangle
Quadrilateral EFGH is a rectangle. If FH = 5x + 4 and GE = 7x – 6, find x.
Answer: 5
Example 4-1c

9. Solve for x and y in the following rectangles A B x 60° 8
Hint: Special Right Triangles x
60° 8
30° D y C A B
2y + 8 x
3x - 8
4y -12 D C 2x
Hint: p is perimeter A B
P = 36 feet x x D 2x C x
Hint: 2 Equations, 2 Variables  Substitution A B 3y
3x -9 D 2y C

10. Quadrilateral LMNP is a rectangle. Find x.
MLP is a right angle, so mMLP = 90°
Angle Addition Theorem
Substitution
Simplify.
Subtract 10 from each side.
Divide each side by 8.
Answer: 10
Example 4-2a

11. Quadrilateral LMNP is a rectangle. Find y.

12. Alternate Interior Angles Theorem
Since a rectangle is a parallelogram, opposite sides are parallel. So, alternate interior angles are congruent.
Alternate Interior Angles Theorem
Substitution
Simplify.
Subtract 2 from each side.
Divide each side by 6.
Answer: 5
Example 4-2d

13. Quadrilateral EFGH is a rectangle.
a. Find x.
b. Find y.
Answer: 7
Answer: 11
Example 4-2e

14. Kyle is building a barn for his horse
Kyle is building a barn for his horse. He measures the diagonals of the door opening to make sure that they bisect each other and they are congruent. How does he know that the corners are angles?
We know that A parallelogram with congruent diagonals is a rectangle. Therefore, the corners are angles.
Answer:
Example 4-3a

15. Quadrilateral Characteristics Summary
Convex Quadrilaterals
4 sided polygon
4 interior angles sum to 360
4 exterior angles sum to 360
Parallelograms
Trapezoids
Bases Parallel
Legs are not Parallel
Leg angles are supplementary
Median is parallel to bases Median = ½ (base + base)
Opposite sides parallel and congruent
Opposite angles congruent
Consecutive angles supplementary
Diagonals bisect each other
Rectangles
Rhombi
Isosceles Trapezoids
All sides congruent
Diagonals perpendicular
Diagonals bisect opposite angles
Angles all 90°
Diagonals congruent
Legs are congruent
Base angle pairs congruent
Diagonals are congruent
Squares
Diagonals divide into 4 congruent triangles

16. Summary & Homework Summary: Homework:
A rectangle is a quadrilateral with four right angles and congruent diagonals
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle
Homework:
pg ; , 16-20, 42