pair of parallel sides. The parallel sides are the bases. The nonparallel sides are the legs.
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1 age 1 of rapezoids Goal Use properties of trapezoids. trapezoid is a quadrilateral with eactly one pair of parallel sides. he parallel sides are the bases. he nonparallel sides are the legs. leg base leg Key Words trapezoid bases, legs, and base angles of a trapezoid isosceles trapezoid idsegent of a trapezoid trapezoid has two pairs of base angles. In trapezoid, a and a are one pair of base angles. a and a are the other pair. If the legs of a trapezoid are congruent, then the trapezoid is an. isosceles trapezoid base isosceles trapezoid HEOE 6.1 and 6.1 heore 6.1 Words If a trapezoid is isosceles, then each pair of base angles are congruent. ybols In the isosceles trapezoid, aca and aca. heore 6.1 Words If a trapezoid has a pair of congruent base angles, then it is isosceles. ybols In trapezoid, if aca then is isosceles. Visualize It! Q In Eaple 1, fill in the issing angle easures as you find the. EXLE Q is an isosceles trapezoid. Find the issing angle easures. olution 1 Find ngle easures of rapezoids 1 Q is an isosceles trapezoid and a and a are a pair of base angles. o, a a. ecause a and a are sae-side interior angles fored by parallel lines, they are suppleentary. o, a ecause aq and a are a pair of base angles of an isosceles trapezoid, aq a 10. hapter 6 Quadrilaterals
2 age of 5 Find ngle easures of rapezoids is an isosceles trapezoid. Find the issing angle easures tudent Help VOULY I he idsegent of a trapezoid is soeties called the edian of a trapezoid. idsegents he idsegent of a trapezoid is the segent that connects the idpoints of its legs. he idsegent of a trapezoid is parallel to the bases. he length of the idsegent idsegent of a trapezoid is half the su of the lengths of the bases. 1 ( ) EXLE idsegent of a rapezoid Find the length of the idsegent G &** of trapezoid EFH. olution E 8 F G Use the forula for the idsegent of a trapezoid. 0 H G 1 (EF H) Forula for idsegent of a trapezoid 1 (8 0) ubstitute 8 for EF and 0 for H. 1 (8) 14 dd. ultiply. WE he length of the idsegent G &** is 14. idsegent of a rapezoid Find the length of the idsegent &** of the trapezoid rapezoids
3 age of Eercises Guided ractice Vocabulary heck 1. ae the bases of trapezoid.. ae the legs of trapezoid. kill heck ecide whether the quadrilateral is a trapezoid, an isosceles trapezoid, or neither Find the length of the idsegent ractice and pplications Etra ractice ee p arts of a rapezoid atch the parts of trapezoid Q with the correct description. 9. Q &* and &* 10.aQ and a. legs. base angles 11. a and aq. opposite angles 1. &**. bases 1. Q&* and &* E. idsegent Hoework Help Eaple 1: Es Eaple : Es. 0 6 Finding ngle easures JKL is an isosceles trapezoid. Find the issing angle easures. 14. K L 15. K L 16. L J K J J 18 4 hapter 6 Quadrilaterals
4 age 4 of 5 Finding ngle easure Q is a trapezoid. Find the issing angle easures Finding idsegents Find the length of the idsegent &** of the trapezoid Using lgebra Find the value of ake esign 1 6. ake esign he top layer of the cake in the diagra at the right has a diaeter of 10 inches. he botto layer has a diaeter of inches. What is the diaeter of the iddle layer? 10 in. in. KE EIGE for and sculpt shapes and figures onto cakes by using tools such as icing bags, handade paper cones, or cutters. oordinate Geoetry he vertices of a trapezoid are (, 6), (8, 6), (8, ), and (4, ). 7. lot the vertices on a coordinate plane. onnect the to for trapezoid. 8. ae the bases of trapezoid. 9. ae the legs of trapezoid. 0. Find the coordinates of the idpoint of each leg. hen plot these points on the coordinate plane you drew in Eercise 7. What is the line segent that connects these two points called? 6.5 rapezoids 5
5 age 5 of 5 Itudent Help I L Z O E. O HOEWOK HEL Etra help with proble solving in Es. 1 is at classzone.co Visualize It! In Eercises 1, use the figures shown below. he figure on the left is a trapezoid with idsegent of length. he figure on the right is fored by cutting the trapezoid along its idsegent and rearranging the two pieces Which theore or postulate fro hapter can you use to show that a1 ca and a ca4 in the figure on the left?. What kind of quadrilateral is on the right? Eplain your answer.. hallenge How does the diagra help you see that the length of the idsegent is half the su of the lengths of the bases? tandardized est ractice 4. ultiple hoice In the trapezoid at the right, what is the value of? 1 15 J K L 5. ultiple hoice Which of the following ust a trapezoid have? F congruent bases G diagonals that bisect each other H eactly one pair of parallel sides J a pair of congruent opposite angles ied eview Logical easoning ell whether the quadrilateral is a parallelogra. Eplain your reasoning. (Lesson 6.) lgebra kills ultiplying ultiply. Write the answer in siplest for. (kills eview, p. 659) hapter 6 Quadrilaterals
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" Angles ABCand DEFare congruent
Collinear points a) determine a plane d) are vertices of a triangle b) are points of a circle c) are coplanar 2. Different angles that share a common vertex point cannot a) share a common angle side! b)
Geometry Review Flash Cards
point is like a star in the night sky. However, unlike stars, geometric points have no size. Think of them as being so small that they take up zero amount of space. point may be represented by a dot on
Areas of Circles and Sectors. GO for Help
-7 What You ll Learn To find the areas of circles, sectors, and segments of circles... nd Why To compare the area of different-size pizzas, as in Example reas of ircles and Sectors heck Skills You ll Need
CCGPS UNIT 3 Semester 1 ANALYTIC GEOMETRY Page 1 of 32. Circles and Volumes Name:
GPS UNIT 3 Semester 1 NLYTI GEOMETRY Page 1 of 3 ircles and Volumes Name: ate: Understand and apply theorems about circles M9-1.G..1 Prove that all circles are similar. M9-1.G.. Identify and describe relationships
Geometry. Higher Mathematics Courses 69. Geometry
The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and
Right Triangles 4 A = 144 A = 16 12 5 A = 64
Right Triangles If I looked at enough right triangles and experimented a little, I might eventually begin to notice a relationship developing if I were to construct squares formed by the legs of a right
Geometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter