1 / 6

EXAMPLE 2

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

kata
Download Presentation

EXAMPLE 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Arch The stone above the arch in the diagram is an isosceles trapezoid. Find mK, mM, and mJ. STEP 1 Find mK. JKLMis an isosceles trapezoid, so Kand Lare congruent base angles, and mK = mL= 85o. EXAMPLE 2 Use properties of isosceles trapezoids SOLUTION

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

  3. In the diagram,MNis the midsegment of trapezoidPQRS. FindMN. SOLUTION Use Theorem 8.17 to findMN. 1 =(12+ 28) 2 1 MN (PQ + SR) = 2 ANSWER The length MNis 20 inches. EXAMPLE 3 Use the midsegment of a trapezoid Apply Theorem 8.17. Substitute 12 for PQand 28 for XU. = 20 Simplify.

  4. 3. If EG = FH, is trapezoid EFGHisosceles? Explain. ANSWER yes, Theorem 8.16 for Examples 2 and 3 GUIDED PRACTICE In Exercises 3 and 4, use the diagram of trapezoidEFGH.

  5. 4. If mHEF = 70o and mFGH =110o, is trapezoid EFGHisosceles? Explain. SAMPLE ANSWER Yes; mEFG =70° by Consecutive Interior Angles Theorem making EFGH an isosceles trapezoidby Theorem 8.15. for Examples 2 and 3 GUIDED PRACTICE

  6. J K 9 cm ANSWER 12 cm P N M L 1 2 15 cm; Solve for x to find ML. ( 9 + x ) = 12 for Examples 2 and 3 GUIDED PRACTICE 5. In trapezoid JKLM, Jand M are right angles, and JK = 9 cm. The length of the midsegment NPof trapezoid JKLMis 12 cm. Sketch trapezoid JKLMand its midsegment. Find ML. Explain your reasoning.

More Related