Question

geometry worksheet – substitute day
topics covered

• segment relationships
• angle relationships (vertical, linear pair, complementary, supplementary)
• parallel, perpendicular, and skew lines

part a: segment relationships (1–10)
use the diagram for each problem.

1. segment ab = 6 cm and bc = 10 cm.

if point b is between a and c, find ac.

1. segment de = 18 cm. point f divides the segment so df = ef.

find df.

1. segment gh = 3x + 4 and hj = 2x + 10.

if gh = hj, find x.

1. segment lm = 4x − 2 and mn = x + 10.

if l, m, n are collinear and lm + mn = 36, find x.

1. if pq = 15 cm, pr = 9 cm, and r is between p and q, find rq.
2. two segments are congruent. one measures 11 cm.

what is the length of the other?

1. segment ab = 5x, segment cd = 20.

if the segments are congruent, find x.

1. point m is the midpoint of segment xy. if xy = 24 cm, find xm.
2. segment ef = 7x + 1, segment fg = 3x + 13.

if e, f, g are collinear and ef = fg, find x.

1. segment jk = 4 cm. segment kl = 3× jk.

find jl.

Explanation:

Problem 1:

Step1: Apply segment addition postulate

Since \( B \) is between \( A \) and \( C \), \( AC = AB + BC \).

Step2: Substitute values

\( AB = 6 \, \text{cm} \), \( BC = 10 \, \text{cm} \), so \( AC = 6 + 10 \).

Step1: Recognize midpoint (since \( DF = EF \))

If \( F \) divides \( DE \) such that \( DF = EF \), then \( F \) is the midpoint, so \( DF=\frac{DE}{2} \).

Step2: Substitute \( DE = 18 \, \text{cm} \)

\( DF=\frac{18}{2}=9 \, \text{cm} \).

Step1: Set \( GH = HJ \)

Given \( GH = 3x + 4 \) and \( HJ = 2x + 10 \), so \( 3x + 4 = 2x + 10 \).

Step2: Solve for \( x \)

Subtract \( 2x \) and \( 4 \) from both sides: \( 3x - 2x = 10 - 4 \), so \( x = 6 \).

Answer:

\( 16 \, \text{cm} \)

Problem 2: