4. Given: ABCD is a rhombus and AD 1 DCProve: ABCD is a squareABStatementReason

Answered: 4. Given: ABCD is a rhombus and AD I DC…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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3. In the accompanying diagram, BDE, AB || CD, and DC bisects LADE. Triangle ABD must be (1) scalene (2) isosceles (3) equiangular (4) right D. AB
2. Quadrilateral MORE is a rhombus with diagonal OE. Which statement will complete the two-column proof to prove that 21= 4 and 22 = 3? * Statement Reason 1. Quadrilateral MORE i n rhombus with diagonal 0E 2. MO ME, RO RE MO I ER, ME I OR 3. AMOE, and AREO are inosceles triangles 1. Given 2. Definition of a rhombun 3. Definition of InOscelen trinngle 4. 5. Definition nf transversal line 6. Altermate interior angles 4. 5. D6 in a tranaversal line 6. 234 7. 214, 22= 3 are congriuent 7. Trannitive Property A. 4. 21 = 2, z3 = 4 | 4. Alternate interior angles are congruent. B. 4. 21 = 23, 24 = L2|4. Opposite angles of congruent sides of an isosceles A are congruent. C. 4. 21 = 4, 22 = 23 | 4. Base O angles of an isosceles A are congruent. D. 4. EM = ER , MO = OR | 4. Definition of congruent triangles.
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Given ABCD is a square, match all congruent parts. D E AD AC CE ABD AED B #CED #AB BD #AE BDC
ABC is a triangle and three squares BCDE, ACFG, ABHK are constructed on its sides outside the triangle. Show that (i) AB² + AD² — АС? + AE?; (ії) GK? + СВ + BG? + CH? = AE² + = 3 (AB? + BC2 + AC²); (v) area of hexagon GKHEDF = 4 AABC + (АВ? + ВС2+ AC?). — 2 (АВ? + AС?) ; (ії) АD? + BF2 + CK² ; (iv) GK² + HE² + DF² %3D %3D Draw AMN BC, DE and AP I GK. Produce PA and draw CQ, BR _s to it
If AD is perpendicular bisector of BE, which statement is true?
Brandon uses the following reasoning to find the length c of the third side in the triangle shown. The two legs of the triangle are 5 and 12. I know by the Pythagorean Theorem that 5 + 12 = , I calculate 5 + 12 = 25 + 144 = 169. My calculator says that the square root of 169 is 13, so c = 13." 67 249 12 Which statement is true about this reasoning? A. Brandons reasoning is conect. B. The Pythagorean Theorem does not apply to this triangle. C. The Pychagorean Theonem applies. but Brandon made a ca culation error. D. It is true that c = 13, but Brandon's reason ng s incorrect because he used a calculator.

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4. Given: ABCD is a rhombus and AD I DC Prove: ABCD is a square A B Statement Reason D