Lesson 8 4 Rectangles 5 Minute Check on
- Slides: 16
Lesson 8 -4 Rectangles
5 -Minute Check on Lesson 8 -3 Transparency 8 -4 Determine whether each quadrilateral is a parallelogram. Justify your answer. 1. 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 5. Standardized Test Practice: Which set of statements will prove LMNO a parallelogram? O L A LM // NO and LO MN B LO // MN and LO MN C LM LO and ON MN D LO MN and LO ON Click the mouse button or press the Space Bar to display the answers. M N
5 -Minute Check on Lesson 8 -3 Transparency 8 -4 Determine whether each quadrilateral is a parallelogram. Justify your answer. Yes, diagonal bisect each other 1. Yes, opposite angles congruent 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 Yes, opposite sides equal No, RS not // UT 5. Standardized Test Practice: Which set of statements will prove LMNO a parallelogram? O L A LM // NO and LO MN B LO // MN and LO MN C LM LO and ON MN D LO MN and LO ON Click the mouse button or press the Space Bar to display the answers. M N
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
Vocabulary • Rectangle – quadrilateral with four right angles.
Polygon Hierarchy Polygons Quadrilaterals Parallelograms Rectangles Rhombi Squares Kites Trapezoids Isosceles Trapezoids
Quadrilateral RSTU is a rectangle. If RT = 6 x + 4 and SU = 7 x - 4 find x. The diagonals of a rectangle are congruent, so Definition of congruent segments Substitution Subtract 6 x from each side. Add 4 to each side. Answer: 8
Quadrilateral EFGH is a rectangle. If FH = 5 x + 4 and GE = 7 x – 6, find x. Answer: 5
Solve for x and y in the following rectangles A B x 60° 8 Hint: Special Right Triangles 30° D A C y 2 y + x 8 4 y - 8 3 x - D A B 12 C B 2 x x D A P = 36 feet x 2 x C x 3 y D Hint: p is perimeter B 3 x -9 2 y C Hint: 2 Equations, 2 Variables Substitution
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
Quadrilateral LMNP is a rectangle. Find y.
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
Quadrilateral EFGH is a rectangle. a. Find x. b. Find y. Answer: 7 Answer: 11
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? Answer: We know that A parallelogram with congruent diagonals is a rectangle. Therefore, the corners are angles.
Quadrilateral Characteristics Summary Convex Quadrilaterals Parallelograms 4 sided polygon 4 interior angles sum to 360 4 exterior angles sum to 360 Opposite sides parallel and congruent Opposite angles congruent Consecutive angles supplementary Diagonals bisect each other Rectangles Trapezoids Bases Parallel Legs are not Parallel Leg angles are supplementary Median is parallel to bases Median = ½ (base + base) Rhombi Angles all 90° Diagonals congruent All sides congruent Diagonals perpendicular Diagonals bisect opposite angles Squares Diagonals divide into 4 congruent triangles Isosceles Trapezoids Legs are congruent Base angle pairs congruent Diagonals are congruent
Summary & Homework • Summary: – 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 428 -429; 10 -13, 16 -20, 42
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