A proof of the Alternate Interior Angles Theorem, using parallel lines a and b with transversal m, is shown below. Given: a b m is the transversal. Prove: 23 = L5 6 Proof: Statements Reasons 1. Lines a and b are parallel with 1. Given transversal m 2. L1 = 25 2. Corresponding Angles Postulate 3. Vertical Angles Theorem 3. 23 = L1 4. 23 = 25 4. Which pronerty i

Q: The Converse of the Corresponding Angles Theorem states that if twO coplanar lines are cut by a…

A: The converse of the corresponding angles theorem states that if two coplanar lines are cut by a…

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Q: The Converse of the Corresponding Angles Theorem states that if two coplanar lines are cut by a…

A: The theorem of converse of correspondingangles :   If two parallel lines are cut by a transversal,…

Q: If m23 = 105°, what is the m/21 that will prove that lines p and r are parallel? %3D 12 56 4/3 8 7…

A: Given: m∠3=105° To find m∠21 such that line p and r are parallel. Solution: If line p and q are…

Q: If AB is parallel to CD, which statement must be true? CD. O A. The perpendicular distance between…

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Q: III. Prove : If two lines are cut by a transversal so as to form a pair of equal alternate interior…

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Q: Exercise no. 5 Given: Line l and line m are perpendicular 22 26 Prove: 25 26

A: Given:  Line l and line m are perpendicular.∠2≅∠6 To Find: To prove ∠5≅∠6

Q: Complete the proof to prove line m and n parallel given 48 = (4x + 25) and6 (5x + 12) and r 13 2 3/6…

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Q: 1. Determine the principal angle for the following angles. a. 540° 137 b. 197 С. 4 2. Determine all…

A: solution written below

Q: Given quadrilateral WXYZ with coordinates W(4, 5), X(9, 4), Y (8,0) and Z(3, 1). Prove or disprove…

A: Quadrilateral is parallelogram if diagonals bisect each other

Q: Which of the following conjectures is true for all cases about the lines in the image shown? A. If…

A: If two lines are cut by a transversal and,  if , Corresponding angles are congruent(i.e. equal),…

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Q: Let ABCD be a rectangle. The perpendicular bisector of the line segment BD intersects lines AB and…

A: let ABCD be a rectangle with vertex B at origin. let EF is the perpendicular bisector of line BD…

Q: NC3,2)

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Q: 1. Use the diagram below to answer the following questions. a) Name all segments parallel to XT b)…

A: There are given diagrams. We have to describe the relationship as parallel, intersecting or skew for…

Q: e. Make a conjecture about the measures of the angles created when a line intersects two parallel…

A: Here is the solution of the given problem. Different Type of Conjecture when two parallel lines cut…

Q: Which construction of parallel lines is justified by the theorem “When two lines are intersected by…

A: *to find:- to find the correct diagram which justifies the given theorem.

Q: 3. In the figure below AB, is parallel to tD. A 4/3 B 5/6 8/7 D Which statement proves that 23 = 47?…

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Q: the measures of uie oIe pe For numbers 5 -8. Refer to the figure at the right 5. What segment is…

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Q: a plane quadrilateral ond E drawn paralle I t is drawn in G. Prove that ABCD • Pont on AD is IS EF…

A: Given : ABCD is a plane quadrilateral and E is any point on AD.  EF is drawn parallel to DB to meet…

Q: The Converse of the Corresponding Angles Theorem states that if two coplanar lines are cut by a…

A: The converse of the corresponding angles theorem states that if two coplanar lines are cut by a…

Q: The perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a…

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Q: A proof of the Alternate Interior Angles Theorem, using parallel lines a and b with transversal m,…

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Q: Use the diagram below to answer the question. 1/2 3/4 87 6/5 Given /1 /5, which theorem proves the…

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Q: Use the diagram below to answer the question. 1/2 3 4 8 7 6/5 Given 2 + 3 = 180", which theorem…

A: The figure is

Q: Complete the proof to prove line m and n parallel given 8 = (4x +25) and6 (5x + 12) and z = 13 m 3/6…

A: 1. The Statement 1 will be  ∠8=4x+25° and ∠6=5x+12° and x=13 and the reason will be given. 2. The…

Q: Given two sets of parallel lines in the diagram below, what is the relationship between Đ6 and Đ15?…

A: Question is related to angle of parallel lines.

Q: In part (a), prove that h || k. In parts (b) and (c), solve for x given that q || p and s || r,…

A: topic - lines and angles

Q: Let AC and BD be two line segments that bisect each other at E, with AC & BD. Prove that ABCD......…

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Q: In the figure, m | n, and line r is a transversal of lines m and n. 5 8 7 What justifies the…

A: we will use the concept of pair of angles formed by parallel lines and transversal line

Q: Use the diagram below to answer the question. 1/2 8/7 3 4 6/5 Given Z12 25, which theorem proves the…

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Q: Label a point D outside AABC so that AD WY and ZDAB ZYWX. Since WX AB, AWXY AABD by Now, let E be…

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Q: 2. Determine the measure of the indicated angle from the figure on the right; given lines l and m…

A: Solve by properties of angles

Q: 1 The diagram below shows the construction of AB ( through point P parallel to CD. P B C Which…

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Q: We have learned how to "drop a perpendicular" from a point to a line using our unruled straightedge…

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Q: Use the diagram below to answer the question. 1/2 3/4 87 6 5 Given Z1 5, which theorem proves the…

A: Given: ∠1≅∠5

Q: Complete the proof that if parallel lines are cut by a transversal, then same-side exterior angles…

A: Explained below

Q: If PR bisects ZSRT and U is the midpoint of RT, classify each triangle by its angles and sides. 15.…

A: The triangles are drawn in the figure given in the problem. 15. △UQR The sides and angles of △UQR,…

Q: Below is a two-column proof incorrectly proving that the three angles of APQR add up to 180°:…

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Q: Let AC and BD be two line segments that bisect each other at E, with AC & BD. Prove that ABCD......…

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Q: Indicate whether the statement is true or false. If coplanar lines r and s are cut by transversal t…

A: True

Q: Given  m∠14+m∠3=180° . Which lines are parallel, if any must be parallel, based on the given…

A: Given  m∠14+m∠3=180° .

Q: EXERCISES 1. Prove Playfair's postulate equivalent to the alternate interior angle theorem: If two…

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Q: Jordan has to prove the theorem that states: If two lines are cut by a transversal so that…

A: They must choose contradiction so as to get a contraduction in thw given statement.

Q: Given: mzAEB = 90°, E is the C midpoint of both AC and BD Prove: <BDC4ABD 3. A D Statements Reasons…

A: Given: m∠AEB=90°    ……1 E is the midpoint of both AC and BD    ……2   To prove: ∠BDC≅∠ABD

Q: Prove that segment AC bisects segment BD, and that segment BD bisects segment AC using the ASA…

A: Explanation: We will set up the statements in following order:

Q: Let ABC be a triangle and let X and Y be points on AB and AC, respectively. Let AX = 6AY = 3, XB=1,…

A: Given information: ABC be a triangle and let X and Y be points on AB and AC, respectively. AX=6,…

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A: Draw a line parallel to bisector line AD to meet line AC at E

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