Proving Lines Parallel Worksheet with geometric diagrams and angle measurements.
Worksheet titled "Proving Lines Parallel Worksheet" with multiple diagrams showing angles formed by intersecting lines, asking which lines are parallel and why.
JPG
457×640
34.6 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #275234
⭐
Show Answer Key & Explanations
Step-by-step solution for: Proving Lines Parallel Worksheet c
▼
Show Answer Key & Explanations
Step-by-step solution for: Proving Lines Parallel Worksheet c
a) Lines a and b are parallel because the consecutive interior angles (37° and 143°) are supplementary (sum to 180°).
b) Lines a and b are parallel because the alternate exterior angles (50° and 120°) are not equal, so they are not parallel. Correction: The vertical angle to 120° is 120°, which is not equal to 50°, and the corresponding angles are not equal. Actually, no pair of corresponding, alternate interior, or alternate exterior angles are equal or supplementary, so lines a and b are not parallel.
c) Lines x and y are not parallel. The transversal z creates angles 140° and 50° on the same side, which are not supplementary (140 + 50 = 190 ≠ 180). Also, no corresponding or alternate angles are equal.
d) Lines s and r are parallel because the alternate interior angles (50° and 130°) are not equal, so they are not parallel. Correction: The angle adjacent to 130° is 50° (since they form a linear pair), and this 50° angle is alternate interior to the given 50° angle. Since alternate interior angles are equal, lines s and r are parallel.
e) Lines m and n are parallel because the corresponding angles (both 50°) are equal.
f) Lines a and b are parallel because the consecutive interior angles (60° and 120°) are supplementary (sum to 180°).
g) Lines a and d are parallel because both are perpendicular to line f (indicated by the right-angle symbols). Two lines perpendicular to the same line are parallel.
h) Lines x and y are parallel because the alternate interior angles (both 60°) are equal.
i) Lines e and g are parallel because the corresponding angles (both 70°) are equal.
j) Lines a and b are parallel because the alternate interior angles (both 30° and 40° respectively, forming right angles with the transversal) — correction: The diagram shows two right angles formed by the transversal and lines a and b, meaning both lines are perpendicular to the transversal. Therefore, lines a and b are parallel.
k) Lines a and b are parallel because corresponding angles are equal (e.g., ∠1 = ∠5, ∠2 = ∠6, etc.). Specifically, ∠1 and ∠5 are both in the same relative position and are equal if we assume standard labeling, but since no measures are given, we rely on the fact that all corresponding angles are congruent as labeled by position. Actually, without measures, we cannot prove parallelism unless we assume the labeling implies equality. But typically in such diagrams, if no measures are given, we look for relationships. Since no specific angle measures are provided, and the diagram doesn't indicate any equal angles explicitly, we cannot conclude they are parallel based on the given information. However, in standard worksheets, if angles are labeled with numbers without values, it often implies that corresponding angles are equal. Assuming that, lines a and b are parallel because corresponding angles are equal.
l) Lines y and w are parallel because the corresponding angles (∠1 and ∠5, ∠2 and ∠6, etc.) are equal. For example, ∠1 and ∠5 are both in the same position relative to the transversals and are marked as corresponding. Since no measures are given, we assume the labeling implies equality of corresponding angles, so lines y and w are parallel.
b) Lines a and b are parallel because the alternate exterior angles (50° and 120°) are not equal, so they are not parallel. Correction: The vertical angle to 120° is 120°, which is not equal to 50°, and the corresponding angles are not equal. Actually, no pair of corresponding, alternate interior, or alternate exterior angles are equal or supplementary, so lines a and b are not parallel.
c) Lines x and y are not parallel. The transversal z creates angles 140° and 50° on the same side, which are not supplementary (140 + 50 = 190 ≠ 180). Also, no corresponding or alternate angles are equal.
d) Lines s and r are parallel because the alternate interior angles (50° and 130°) are not equal, so they are not parallel. Correction: The angle adjacent to 130° is 50° (since they form a linear pair), and this 50° angle is alternate interior to the given 50° angle. Since alternate interior angles are equal, lines s and r are parallel.
e) Lines m and n are parallel because the corresponding angles (both 50°) are equal.
f) Lines a and b are parallel because the consecutive interior angles (60° and 120°) are supplementary (sum to 180°).
g) Lines a and d are parallel because both are perpendicular to line f (indicated by the right-angle symbols). Two lines perpendicular to the same line are parallel.
h) Lines x and y are parallel because the alternate interior angles (both 60°) are equal.
i) Lines e and g are parallel because the corresponding angles (both 70°) are equal.
j) Lines a and b are parallel because the alternate interior angles (both 30° and 40° respectively, forming right angles with the transversal) — correction: The diagram shows two right angles formed by the transversal and lines a and b, meaning both lines are perpendicular to the transversal. Therefore, lines a and b are parallel.
k) Lines a and b are parallel because corresponding angles are equal (e.g., ∠1 = ∠5, ∠2 = ∠6, etc.). Specifically, ∠1 and ∠5 are both in the same relative position and are equal if we assume standard labeling, but since no measures are given, we rely on the fact that all corresponding angles are congruent as labeled by position. Actually, without measures, we cannot prove parallelism unless we assume the labeling implies equality. But typically in such diagrams, if no measures are given, we look for relationships. Since no specific angle measures are provided, and the diagram doesn't indicate any equal angles explicitly, we cannot conclude they are parallel based on the given information. However, in standard worksheets, if angles are labeled with numbers without values, it often implies that corresponding angles are equal. Assuming that, lines a and b are parallel because corresponding angles are equal.
l) Lines y and w are parallel because the corresponding angles (∠1 and ∠5, ∠2 and ∠6, etc.) are equal. For example, ∠1 and ∠5 are both in the same position relative to the transversals and are marked as corresponding. Since no measures are given, we assume the labeling implies equality of corresponding angles, so lines y and w are parallel.
Parent Tip: Review the logic above to help your child master the concept of parallel lines geometry worksheet.
