Theorems Involving Parallel Lines Section 5 3 Goals

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Theorems Involving Parallel Lines Section 5 -3

Theorems Involving Parallel Lines Section 5 -3

Goals • We will apply theorems about parallel lines and the segment that joins

Goals • We will apply theorems about parallel lines and the segment that joins the midpoints of two sides of a triangle.

Theorem 5 -8 • If two lines are parallel, then all points on one

Theorem 5 -8 • If two lines are parallel, then all points on one line are equidistant to the other line. 5 ft

Theorem 5 -9 • If three parallel lines cut off congruent segments on one

Theorem 5 -9 • If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Practice Find the values of x and y if P is the midpoint of

Practice Find the values of x and y if P is the midpoint of AB 3 x – 14 2 x – 1 2 y + 10 A 6 y – 30 P B

Practice Find the values of x and y if P is the midpoint of

Practice Find the values of x and y if P is the midpoint of AB 3 x – 14 = 2 x – 14 = -1 x = 13 3 x – 14 2 x – 1 2 y + 10 = 6 y – 30 10 = 4 y – 30 40 = 4 y 10 = y y = 10 2 y + 10 A 6 y – 30 P B

Practice (Example 1 on sheet) AR BS CT, and RS = ST R A

Practice (Example 1 on sheet) AR BS CT, and RS = ST R A S B T C Complete: a. if RS = 12, then ST = ____ b. if AB = 8, then BC = ____ c. if AC = 20, then AB = ____ d. if AC = 10 x, then BC =____

Theorem 5 -10 • A line that contains the midpoint of one side of

Theorem 5 -10 • A line that contains the midpoint of one side of a triangle, and is parallel to another side, will pass through the midpoint of the third side. parallel

Theorem 5 -11 • A segment that joins the midpoints of two sides of

Theorem 5 -11 • A segment that joins the midpoints of two sides of a triangle: 1. ) is parallel to the third side 2. ) is half as long as the third side

Practice Find the value of w and z. (3 z + 1)cm 38˚ 8

Practice Find the value of w and z. (3 z + 1)cm 38˚ 8 cm 2 w˚ 70˚

Practice Find the value of w and z. (3 z + 1)cm w =

Practice Find the value of w and z. (3 z + 1)cm w = 36 z=5 38˚ 8 cm 2 w˚ 70˚

Practice (Example 2 on sheet) R, S, and T are midpoints of the sides

Practice (Example 2 on sheet) R, S, and T are midpoints of the sides of triangle ABC B S R A C T Complete the table. AB BC AC 12 14 18 15 22 10 ST RT RS 9 7. 8 10

Practice R, S, and T are midpoints of the sides of triangle ABC B

Practice R, S, and T are midpoints of the sides of triangle ABC B S R A C T Complete the table. AB BC AC ST RT RS 12 14 18 6 7 9 20 15 22 10 7. 5 11 10 18 15. 6 5 9 7. 8 Back to Parallelograms

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