EXAMPLE 2 Use properties of isosceles trapezoids Arch

Slides:

Advertisements

Similar presentations

Lesson 6-6 Trapezoids and Kites

Advertisements

6.5 Trapezoids and Kites Geometry Mrs. Spitz Spring 2005.

8.6 Trapezoids.

Lesson 8-6 Trapezoids Theorem 8.18

Trapezoids & Kites. Trapezoid Is a quadrilateral with exactly 1 pair of parallel sides.

EXAMPLE 2 Use properties of isosceles trapezoids Arch The stone above the arch in the diagram is an isosceles trapezoid. Find m K, m M, and m J. SOLUTION.

Quadrilaterals.

CP Geometry Mr. Gallo. What is a Trapezoid Trapezoid Isosceles Trapezoid leg Base Base Angles leg Base Angles If a quadrilateral is a trapezoid, _________________.

8.5 Use properties of kites and trapezoids

Use Properties of Trapezoids and Kites Goal: Use properties of trapezoids and kites.

6.6 Trapezoids and Kites A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides of a trapezoid are called bases. The.

Trapezoids and Kites Chapter 6 Section 6 Tr.

6-6 Trapezoids and Kites.

Trapezoids and Kites Section 8.5.

EXAMPLE 1 Identify quadrilaterals Quadrilateral ABCD has at least one pair of opposite angles congruent. What types of quadrilaterals meet this condition?

Chapter 8: Quadrilaterals

6-3 Proving That a Quadrilateral Is a Parallelogram

EXAMPLE 1 Identify quadrilaterals Quadrilateral ABCD has at least one pair of opposite angles congruent. What types of quadrilaterals meet this condition?

QuadrilateralsQuadrilaterals 5-2. EXAMPLE 1 Solve a real-world problem Ride An amusement park ride has a moving platform attached to four swinging arms.

5.12Identify Special Quadrilaterals Example 1 Identify quadrilaterals Quadrilateral ABCD has both pairs of opposite sides congruent. What types of quadrilaterals.

Identify Special Quadrilaterals

8.6 Examples Example 1 STUV has at least one pair of consecutive sides that are congruent. What type of quadrilateral meets this condition? (rhombus,

Showing quadrilaterals are parallelograms. Bell Ringer.

6-6 Trapezoids and Kites You used properties of special parallelograms. Apply properties of trapezoids. Apply properties of kites.

5-minute check In a brief paragraph explain all the properties you know about parallelograms. Explain the properties of the following: Rhombus Rectangle.

5.11 Use Properties of Trapezoids and Kites. Vocabulary  Trapezoid – a quadrilateral with exactly one pair of parallel sides. Base Base Angle Leg.

8.5 TRAPEZOIDS AND KITES QUADRILATERALS. OBJECTIVES: Use properties of trapezoids. Use properties of kites.

5.11Properties of Trapezoids and Kites Example 1 Use a coordinate plane Show that CDEF is a trapezoid. Solution Compare the slopes of the opposite sides.

8.5 Trapezoids and Kites. Objectives: Use properties of trapezoids. Use properties of kites.

Geometry Section 8.5 Use Properties of Trapezoids and Kites.

Trapezoids & Kites Sec 6.5 GOALS: To use properties of trapezoids and kites.

Warm-Up Pg ,10,20,23,43,49 Answers to evens: 6.Always 12. Always 36. About About

Geometry Section 6.5 Trapezoids and Kites. A trapezoid is a quadrilateral with exactly one pair of opposite sides parallel. The sides that are parallel.

6-6 Trapezoids and Kites Objective: To verify and use properties of trapezoids and kites.

6.5: TRAPEZOIDS AND KITES OBJECTIVE: TO VERIFY AND USE PROPERTIES OF TRAPEZOIDS AND KITES.

7.5 Trapezoids and Kites. Trapezoids Definition- A quadrilateral with exactly one pair of parallel sides. Bases – Parallel sides Legs – Non-parallel sides.

Goal: Identify special quadrilaterals

The parallel sides of a trapezoid are called bases.

EXAMPLE 1 Identify congruent angles SOLUTION By the Corresponding Angles Postulate, m 5 = 120°. Using the Vertical Angles Congruence Theorem, m 4 = 120°.

8.5 – Use Properties of Trapezoids and Kites. Trapezoid: Consecutive interior angles are supplementary A B C D m  A + m  D = 180° m  B + m  C = 180°

Properties of Parallelograms Definition  Parallelogram – a quadrilateral with both pairs of opposite sides parallel.

TrapezoidsTrapezoids 5-5. EXAMPLE 1 Use a coordinate plane Show that ORST is a trapezoid. SOLUTION Compare the slopes of opposite sides. Slope of RS =

5.4 Quadrilaterals Objectives: Review the properties of quadrilaterals.

6.5 Trapezoids. Objectives: Use properties of trapezoids.

Use Properties of Trapezoids and Kites Lesson 8.5.

Trapezoids Section 6.5. Objectives Use properties of trapezoids.

6.5 Trapezoids and Kites Homework: the last 4 slides 1 of 21.

Holt Geometry 6-3 Conditions for Parallelograms 6-3 Conditions for Parallelograms Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.

Section 6-5 Trapezoids and Kites. Trapezoid A quadrilateral with exactly one pair of parallel sides.

Bell Ringer. Trapezoid A Trapezoid is a quadrilateral with exactly one pair of parallel sides. The Parallel sides are the bases The non parallel sides.

8.5 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Use Properties of Trapezoids and Kites.

Day 2 Trapezoids. Concept 1 Example 1A Use Properties of Isosceles Trapezoids A. BASKET Each side of the basket shown is an isosceles trapezoid. If m.

6.5 TRAPEZOIDS OBJECTIVE: USE PROPERTIES OF TRAPEZOIDS.

8.5 Use Properties of Trapezoids and Kites Hubarth Geometry.

6.5 EQ: How do you Identify a trapezoid and apply its properties

Use the figure to answer the questions.

Properties of Trapezoids and Kites

6.5 Trapezoids.

Trapezoids and Kites Section 7.5.

Find the value of x ANSWER 65 ANSWER ANSWER 70.

Chapter 8.5 Notes: Use Properties of Trapezoids and Kites

Properties of Trapezoids and Kites

1. What are the values of x and y?

1. What are the values of x and y?

6.5 EQ: How do you Identify a trapezoid and apply its properties?

Tear out pages do problems 5-7, 9-13 I will go over it in 15 minutes!

Understand, use and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

#18 y + 8 = 3y #28 2y = 10 #32 #38 #48 (On next slide)

Goal: The learner will use properties of trapezoids and kites.

Presentation transcript:

EXAMPLE 2 Use properties of isosceles trapezoids Arch The stone above the arch in the diagram is an isosceles trapezoid. Find m K, m M, and m J. SOLUTION STEP 1 Find m K. JKLM is an isosceles trapezoid, so K and L are congruent base angles, and m K = m L= 85o.

EXAMPLE 2 Use properties of isosceles trapezoids STEP 2 Find m M. Because L and M are consecutive interior angles formed by LM intersecting two parallel lines,they are supplementary. So,m M = 180o – 85o = 95o. STEP 3 Find m J. Because J and M are a pair of base angles, they are congruent, and m J = m M =95o. ANSWER So, m J = 95o, m K = 85o, and m M = 95o.

Use the midsegment of a trapezoid EXAMPLE 3 Use the midsegment of a trapezoid In the diagram, MN is the midsegment of trapezoid PQRS. Find MN. SOLUTION Use Theorem 8.17 to find MN. MN (PQ + SR) 1 2 = Apply Theorem 8.17. = (12 + 28) 1 2 Substitute 12 for PQ and 28 for XU. = 20 Simplify. ANSWER The length MN is 20 inches.

GUIDED PRACTICE for Examples 2 and 3 In Exercises 3 and 4, use the diagram of trapezoid EFGH. 3. If EG = FH, is trapezoid EFGH isosceles? Explain. ANSWER Yes, trapezoid EFGH is isosceles, if and only if its diagonals are congruent. As, it is given its diagonals are congruent, therefore by theorem 8.16 the trapezoid is isosceles.

GUIDED PRACTICE for Examples 2 and 3 4. If m HEF = 70o and m FGH = 110o, is trapezoid EFGH isosceles?Explain. BHG=110°, as the sum of a quadrilateral is 360° . The base angles are congruent that is, 110° each therefore, the trapezoid is isosceles by theorem 8.15. ANSWER G and F are consecutive interior angles as EF HG. Because FGH=110°, therefore EFG=70° as they are supplementary angles.

NP is the midsegment of trapezoid JKLM. GUIDED PRACTICE for Examples 2 and 3 5. In trapezoid JKLM, J and M are right angles, and JK = 9 cm. The length of the midsegment NP of trapezoid JKLM is 12 cm. Sketch trapezoid JKLM and its midsegment. Find ML. Explain your reasoning. ANSWER NP is the midsegment of trapezoid JKLM. and NP = ( JK + ML) 1 2 J L K M 9 cm 12 cm x cm N P

for Examples 2 and 3 GUIDED PRACTICE 1 NP (JK + ML) = 2 1 12 = (9 + x) Apply Theorem 8.17. = (9 + x) 1 2 12 Substitute = 9 + x 24 Multiply each side by 2 = x 15 Simplify.