Given DH = GF, DH | GF, DHLHE, GFLFEProve ADHE = AGFESTATEMENTSDHGF, DH || GF, DH L HE, GF L FEZDHE and

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Answered: Given DH = GF, DH | GF, DH LHE, GFLFE…

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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VWU 1navC prUVeu timat If twó lines are parallel, then the alternate exterior angles are congruent. Is converse of this true? If you study the proof of Theorem 14 on page 18, it will help you prove Theorem 15 Theorem 15: If a transversal intersects two lines so that alternate exterior angles are congruent, ther the lines are parallel. Complete this proof of Theorem 15. Given: Transversal t intersects lines m and n; L1 = 23. Prove: m ll n. 1. Proof Statements Reasons Tankerraleinterrede lino nads 1. Givcn 2. 2. 3. 4. If a trans, intersects two lines so that cor. Zs are =, then the lines are ll.0.14) 4. . Theorem 12 uses parallel lines to prove that interior angles on the same side of the transversal are sup mentary. To prove Theorem 16, we must prove either alternate interior, corresponding, or alternate ext angles are congruent. If we can do this, then we know the lines are parallel. side of th
Suppose you are given that A, B, C, D, E, F are points satisfying A ∗ B ∗ C, D ∗ E ∗ F, AB ≅ DE, andCB ≅ EF. Prove that AC ≅ DF. Be careful with notation, and justify all steps.
Lines m and n are parallel and k is a transversal. Find x, y, and m<8 if the following are given. m<1=9x+3y m<2=6x+3y m<8= 6x+9y
In the proof below, what statement is needed in line 2 complete the proof? Given: AXY Z Prove: m/1+m22+ m23 = 180* W 4/1 2 Y 3 Statements Reasons 1. Through any point not on a line, there is exactly one line parallel to the given line. 1. Through point X, draw XW so that XW || YŹ 2. 2. Angle Addition Postulate 3. 22 4; 25 23 3. If parallel lines are cut by a transversal, then alternate interior angles are congruent. 4.m/2 = m4; m/5 = m23 4. Definition of congruent angles. 5. m/1+m22 + m/3 180 5. Substitution Property Sign SUS -> 女 @ #3 $ % & 4 7 8. W e r y u i S d f j k
2. G.CO.9 Look at the diagram below showing two parallel lines being cut by two transversals. If m<4 = 70 and m/12 = 130, which of the following statements are true? SELECT ALL THAT APPLY. A. m/1 = 70 B. m/2 = 110 C. m²6 = 70 6 D. m28 = 130 E. m29 = 50 F. m/10 = 50 G. m/13 = 130 H. m2 16 130 8 7 * 16 15 13 14 12 11 9 10
M B. Exterior Angle Inequality Theorem Given: Δ ΜΝΟ Prove: mzM + m2N = M¿ACB Statement Reason 1. ΔΜΝΟ 1. 2. Angle Sum Theorem (The sum of the measures of the interior angles of a 2 triangle is 180°.) 3. MZMON and M
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 of 15 Save Two congruent triangles are one result of a line that is parallel to one side of a triangle and intersects the other two. OTrue O False

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