Lines and Angles

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Answer Key & Explanations

Lines and Angles · Grade 4 · Worksheet 1

1. Ava is drawing a geometric figure. She starts at point A, draws a straight line to point B that is 126 mm long, then continues without stopping to point C, which is another 81 mm away in the same direction. She then stops. What type of geometric figure did Ava draw from point A to point B, and what type from point A to point C? Answer: Line segment from A to B; ray from A to C Solution: Identify the starting and ending points. From A to B, Ava starts at A and stops at B. That means the drawing has two endpoints: A and B.
   Full step-by-step solution

   Step 1: Identify the starting and ending points. From A to B, Ava starts at A and stops at B. That means the drawing has two endpoints: A and B. A figure with two endpoints is a line segment. Step 2: Now look from A to C. Ava starts at A, goes through B, and then stops at C. But notice that the line continues in the same direction beyond B to C. Since she could keep drawing further in that direction, the figure from A to C has one endpoint (A) and goes on forever in the other direction. That is a ray. Step 3: So, the answer is: from A to B is a line segment; from A to C is a ray.

2. Ava is drawing a map of her neighborhood. She draws a straight line from her house to the library, but the line keeps going past the library without an endpoint. She also draws a line from the library to the school that stops exactly at the school. What geometric terms describe the first line (house to beyond the library) and the second line (library to school)? Answer: The first line is a ray, and the second line is a line segment. Solution: Identify the first line. It starts at Ava's house (one endpoint) and continues past the library without ending. Step 2: Identify the second line.
   Full step-by-step solution

   Step 1: Identify the first line. It starts at Ava's house (one endpoint) and continues past the library without ending. That matches the definition of a ray. Step 2: Identify the second line. It starts at the library and ends exactly at the school, so it has two endpoints. That matches the definition of a line segment. Final answer: The first line is a ray, and the second line is a line segment.

3. Sophia is helping her dad build a wooden frame for a large rectangular picture. She notices that the corner of the frame forms a 90-degree angle. Later, she sees the hands of the clock showing 4:00. What type of angle is formed by the clock hands at 4:00? Answer: obtuse angle Solution: Identify the positions of the clock hands at 4:00. The hour hand points at 4, and the minute hand points at 12. Step 2: Imagine or sketch the angle formed.
   Full step-by-step solution

   Step 1: Identify the positions of the clock hands at 4:00. The hour hand points at 4, and the minute hand points at 12. Step 2: Imagine or sketch the angle formed. Step 3: Compare this angle to a right angle (90 degrees). At 4:00, the angle between the hands is 120 degrees, which is greater than 90 degrees. Step 4: An angle greater than 90 degrees but less than 180 degrees is called an obtuse angle. The answer is obtuse angle.

4. Noah is drawing a clock. The hour hand points directly at the number 2, and the minute hand points directly at the number 6. What type of angle is formed between the hour hand and the minute hand on Noah's clock? (Choose from: acute, right, obtuse, or straight.) Answer: straight Solution: Visualize a clock. The numbers are evenly spaced around a circle. Step 2: The number 12 is at the top, 3 is at the right, 6 is at the bottom, and 9 is at the left.
   Full step-by-step solution

   Step 1: Visualize a clock. The numbers are evenly spaced around a circle. Step 2: The number 12 is at the top, 3 is at the right, 6 is at the bottom, and 9 is at the left. Step 3: The hour hand at 2 is two steps past 12. The minute hand at 6 is directly opposite the 12. Step 4: The hands form a straight line going from the 2 o'clock position through the center to the 6 o'clock position. Step 5: An angle that forms a straight line is called a straight angle. The answer is straight.

5. Mason is helping his little sister draw shapes on a chalkboard. First, he draws a straight line that starts at a dot labeled A and goes through a dot labeled B, continuing forever in both directions without any endpoints. Next, his sister draws a straight line that starts at a dot labeled C and ends exactly at a dot labeled D, stopping at both dots. Finally, Mason draws a third straight line that starts at a dot labeled E and goes forever in one direction past a dot labeled F. What three geometric figures did Mason and his sister draw, in order? Answer: line, line segment, ray Solution: The first figure starts at point A, goes through point B, and continues forever in both directions without any endpoints. This is a line because a line extends infinitely in both directions.
   Full step-by-step solution

   Step 1: The first figure starts at point A, goes through point B, and continues forever in both directions without any endpoints. This is a line because a line extends infinitely in both directions. Step 2: The second figure starts at point C and ends exactly at point D, stopping at both points. This has two endpoints, so it is a line segment. Step 3: The third figure starts at point E and goes forever in one direction past point F. This has one endpoint and extends infinitely in one direction, so it is a ray. Step 4: In order, the three geometric figures are: line, line segment, ray. Answer: line, line segment, ray

6. Tane is building a model sailboat for a school project. He draws a large straight line across his paper to represent the horizon. Then, he draws a line that starts at a point on the horizon and goes straight up, making a perfect square corner with the horizon. What type of angle is formed at the point where the vertical line meets the horizon? Answer: D. Right angle Solution: The horizon is a straight line. The vertical line meets it at a point. Step 2: A square corner means the two lines are perpendicular to each other.
   Full step-by-step solution

   Step 1: The horizon is a straight line. The vertical line meets it at a point. Step 2: A square corner means the two lines are perpendicular to each other. Step 3: A perpendicular intersection creates an angle that measures exactly 90 degrees. Step 4: In geometry, a 90-degree angle is called a right angle. The correct answer is Right angle.