10. hailey has a sheet of plywood with four right angles. she saws off one of the angles and turns the plywood one - half turn clockwise. how many right angles are there on the plywood now?

use the information to answer problems 11 - 12.

margot draws a shape with one pair of parallel lines that are four centimeters apart. she then flips the shape across a horizontal line.

11. how many pairs of parallel lines are on the flipped shape?

12. how far apart are the parallel lines on the flipped shape? how do you know?

13. complete each transformation of the given figure.

14. complete the drawing of the parallelogram after a slide to the right.

15. open ended perform a transformation on the shape. draw the result and describe the transformation you performed.

Question

10. hailey has a sheet of plywood with four right angles. she saws off one of the angles and turns the plywood one - half turn clockwise. how many right angles are there on the plywood now?

use the information to answer problems 11 - 12.

margot draws a shape with one pair of parallel lines that are four centimeters apart. she then flips the shape across a horizontal line.

11. how many pairs of parallel lines are on the flipped shape?

12. how far apart are the parallel lines on the flipped shape? how do you know?

13. complete each transformation of the given figure.

14. complete the drawing of the parallelogram after a slide to the right.

15. open ended perform a transformation on the shape. draw the result and describe the transformation you performed.

Accepted Answer

### Problem 10
# Explanation:
## Step1: Analyze the original shape
The original plywood has four right angles, so it's a rectangle (since rectangles have four right angles).
## Step2: Analyze the sawing and turning
When one angle (a right angle) is sawn off, the shape becomes a pentagon? Wait, no. Wait, a rectangle has four right angles. If we saw off one right angle (by cutting a triangle off one corner), the original corner (right angle) is replaced by two new angles. But then we turn the plywood a half - turn (180 degrees) clockwise. Wait, maybe a better way: A rectangle has four right angles. If we cut off one right - angled corner (so we remove a right angle and add two angles), but when we turn it 180 degrees, the number of right angles: Let's think of the rectangle. Suppose we cut off a corner such that we have a new shape. But maybe the key is that a half - turn (rotation by 180 degrees) doesn't change the number of right angles in terms of the angle measures, but the cutting: Wait, maybe the original is a rectangle (4 right angles). When we saw off one angle (a right angle), we are left with 3 right angles? No, wait, when you cut a rectangle's corner (a right angle) with a saw, you are creating a new vertex. The original right angle is split into two angles, but maybe the other three right angles remain? Wait, no, if you cut off one corner of a rectangle, the shape becomes a pentagon. The original four right angles: one is replaced by two angles, so the number of right angles: let's say the rectangle has vertices A, B, C, D with right angles at each. If we cut off corner A (between sides AB and AD) by a line from a point on AB to a point on AD, then the new shape has vertices: on AB: a point E, on AD: a point F, then B, C, D. So the angles at B, C, D are still right angles (since we haven't cut those sides). The angle at E: between BE and EF, and the angle at F: between DF and EF. The original angle at A was 90 degrees, now we have two angles at E and F. But then we turn the plywood 180 degrees clockwise. Rotation by 180 degrees preserves the angle measures. So the number of right angles: the three right angles at B, C, D (after cutting) are still right angles, and what about the other two angles? Wait, maybe I made a mistake. Wait, the problem says "she saws off one of the angles and turns the plywood one - half turn clockwise". A half - turn is 180 degrees. Let's think of the rectangle: four right angles. If we saw off one right angle (so we have a new shape with, say, 5 sides), but when we rotate it 180 degrees, the number of right angles: Let's take a simple case. Suppose the rectangle is square - like. If we cut off a corner (a right angle) to make a pentagon with three right angles (the other two angles are not right angles), then rotating 180 degrees doesn't change the number of right angles. Wait, maybe the answer is 3? No, wait, maybe the original is a rectangle (4 right angles). When you saw off one angle (a right angle), you are left with 3 right angles? No, when you cut a rectangle's corner, you are creating a new edge, so the number of angles increases by 1 (from 4 to 5). The original four right angles: one is replaced by two angles, so the number of right angles is 3 (the other three corners are still right angles). Then, when you turn it 180 degrees, the angle measures remain the same. So the number of right angles is 3? Wait, no, maybe I'm wrong. Wait, let's consider the rectangle. Let's say the rectangle has length L and width W. If we cut off a right - angled triangle from one corner, the new shape has five sides. The three original corners (not the cut one) still have right angles (90 degrees). The two new angles: let's say the cut is such that the two new angles add up to 270 degrees (since the sum of angles in a pentagon is (5 - 2)*180=540 degrees. Original sum of angles in rectangle is 360 degrees. After cutting, we add 180 degrees (the triangle), so 360+180 = 540, which matches the pentagon's angle sum). The three original right angles (90 each) sum to 270, so the remaining two angles sum to 540 - 270=270. So they are not right angles. Then, when we rotate the pentagon 180 degrees, the three right angles are still right angles. So the number of right angles is 3? Wait, but maybe the answer is 3 or 5? Wait, no, maybe I messed up. Wait, the problem says "she saws off one of the angles and turns the plywood one - half turn clockwise". A half - turn is 180 degrees. Let's think differently: the original is a rectangle (4 right angles). If we saw off one angle (a right angle), we now have a shape with, say, 3 right angles? No, when you cut a rectangle's corner, you are left with 3 right angles? Wait, no, a rectangle has four right angles. If you cut off one corner (a right angle) by a straight line, you create a new vertex, so the number of angles becomes 5. The three angles that were not cut are still right angles (90 degrees), and the two new angles: let's assume the cut is from a point on the top side to a point on the left side of the rectangle. The top - left corner (right angle) is cut, so the new angles at the top - cut point and left - cut point: the angle at the top - cut point: between the top side (remaining) and the new cut edge, and the angle at the left - cut point: between the left side (remaining) and the new cut edge. The sum of these two angles is 90 + 90=180? No, the original angle was 90 degrees, and when you cut it, the two new angles add up to 270 degrees (since the sum of angles around a point is 360, and we removed a triangle with angle 90, so 360 - 90 = 270). Wait, maybe the answer is 3. But I'm not sure. Wait, maybe the correct answer is 3 or 5? Wait, no, let's check again. The original has 4 right angles. Saw off one (so we lose one right angle, but gain two angles). Then turn 180 degrees. Rotation preserves angle measures. So the number of right angles: 4 - 1=3? No, because we gained two angles, but they are not right angles. So the number of right angles is 3.

# Answer: 3 (Note: This is a possible answer, the exact answer may depend on the exact way the angle is sawn off, but a common result is 3 right angles)

### Problem 11
# Explanation:
## Step1: Recall the property of reflection
A flip (reflection) is a rigid transformation. Rigid transformations (reflection, rotation, translation) preserve the shape and size of the figure, including the parallel lines.
## Step2: Determine the number of parallel lines
The original shape has one pair of parallel lines. Since reflection preserves the parallelism of lines, the flipped shape will also have one pair of parallel lines.

# Answer: 1

### Problem 12
# Explanation:
## Step1: Recall the property of reflection
Reflection (flipping) is a rigid transformation. Rigid transformations preserve the distance between parallel lines (or any two points) in the figure.
## Step2: Determine the distance
The original parallel lines are four centimeters apart. Since reflection does not change the distance between the parallel lines, the parallel lines on the flipped shape are also four centimeters apart.

# Answer: The parallel lines on the flipped shape are 4 centimeters apart. We know this because a flip (reflection) is a rigid transformation that preserves the distance between parallel lines.

### Problem 13
(Note: Since this is a drawing problem, we can't draw here, but the general approach is to perform the given transformations (which seem to be various rigid transformations like rotation, reflection, or translation) on the original figure. For each sub - figure, identify the type of transformation (e.g., rotation by a certain angle, reflection over a line, translation) and apply it to each vertex of the original figure, then connect the vertices to get the transformed figure.)

### Problem 14
(Note: For sliding (translation) the parallelogram to the right, we need to move each vertex of the parallelogram a certain distance to the right (the same distance for all vertices) and then connect the new vertices to form the translated parallelogram. Since it's a drawing problem, we can't draw here, but the key is to use the property of translation: all points of the figure are moved the same distance in the same direction.)

### Problem 15
(Note: For an open - ended transformation, we can choose a transformation like translation (slide), rotation (turn), or reflection (flip). For example, if we choose translation: we move the shape a certain distance to the right. Then we draw the shape in the new position and describe the transformation as "I performed a translation (slide) of the shape 2 units to the right. The shape's size and shape remain the same, only its position has changed." If we choose rotation: "I rotated the shape 90 degrees clockwise about a given point (e.g., the bottom - left vertex). The shape's size and shape remain the same, but its orientation has changed." If we choose reflection: "I reflected the shape over a vertical line through its center. The shape's size and shape remain the same, and it is a mirror image across the line of reflection." Then we draw the transformed shape according to the chosen transformation.)

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QUESTION IMAGE

Question

Explanation:

Problem 10

Step1: Analyze the original shape

Step2: Analyze the sawing and turning

Step1: Recall the property of reflection

Step2: Determine the number of parallel lines

Step1: Recall the property of reflection

Step2: Determine the distance

Answer:

Problem 11