Grade 7 Angles and Geometric Constructions Practice Test

Correct answer: A

The correct answer is The point is equidistant from the segment endpoints.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Every point on a segment’s perpendicular bisector is equidistant from the two endpoints.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: B

The correct answer is It divides an angle into two congruent angles.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: An angle bisector is a ray that divides an angle into two equal measures.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: C

The correct answer is A compass and a straightedge.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: A compass creates equal arcs and a straightedge draws the required line.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: D

The correct answer is Draw equal arcs from the two intersection points and connect their intersection to the vertex.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Equal arcs from the two side-intersection points locate a point on the angle bisector; connect it to the vertex.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: A

The correct answer is The midpoint of the segment.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: A perpendicular bisector crosses the segment at its midpoint and forms a right angle.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: B

The correct answer is The arc intersection distances that determine the angle.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Matching the arc and chord distances reproduces the same angle measure.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: C

The correct answer is Draw equal-radius arcs from both endpoints and join an arc intersection to the endpoints.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Two equal-radius circles centered at the endpoints meet at a point equidistant from both endpoints.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: D

The correct answer is Draw equal-radius arcs from both endpoints and connect the arc intersections.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: The two arc intersections are equidistant from both endpoints, so the line through them is the perpendicular bisector.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: A

The correct answer is $40^\circ$.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Divide the full angle by 2: $80^\circ\div2=40^\circ$.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: B

The correct answer is $7\text{ cm}$.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Bisecting divides the segment into two equal parts: $14\div2=7$ centimeters.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.