Transformations
Select all the true statements.
A. Two rhombuses with the same side lengths are always congruent.
B. Two squares with the same side lengths are always congruent.
C. Two quadrilaterals with the same side lengths are always congruent.
D. Two rectangles with the same side lengths are always congruent.
E. Two parallelograms with the same side lengths are always congruent.
B, D
Han’s teacher asked him to draw a polygon similar to polygon A. Here is his work. Which explanation shows that polygons A and C are similar to each other?
(Karissa has image)
A. Use a protractor to measure all four angles in polygon A and all four angles in polygon C. Since each angle in polygon A has a matching angle measure in polygon C, the polygons are similar.
B. Since each side in polygon C is three times as long as the corresponding side in polygon A, the figures are similar.
C. Dilate polygon C with center at the upper-left vertex and a scale factor of . Then, translate 7 units to the left. Since polygon C can be taken to polygon A with a dilation followed by a translation, the figures are similar.
D. Dilate polygon C with center at the upper-right corner and a scale factor of 3. Since polygon C can be taken to polygon A with a dilation, the polygons are similar.
C
Select the equation on which the point (10,0) lies.
A. 5x + 2y = 15
B. 2x +4y = 20
C. 3x + 3y = 13
B
What is the solution to 3x + 30 + x = 10 + 2x + 5x + 2?
6
Lines AC and BD intersect at E. What is the measure of angle BEC if DEA is 108-degrees?
108-degrees
Select the true statement.
A. Dilations of an angle must be congruent to the original angle.
B. Dilations of a triangle must be congruent to the original triangle.
C. Dilations of a segment must be congruent to the original segment.
D. Dilations of a circle must be congruent to the original circle.
A
Write an equation for a line that passes through points (-1,6) and (0,4)
y = -2x + 4
Select all the equations that have no solution.
A. x+6=5+x
B. -2(x-3) = -2x+6
C. 4-4x = 3x+2
D. 4(x+1) = 3(x+2)
E. 5 - 3x = -3x+4
A, E
Clare created Figure A. Then she created Figure B by translating Triangle C and then translating Triangle D.
(Karissa has image)
Select all the true statements.
A. Figure A is congruent to Figure B
B. Figure B is a translation of Figure A.
C. Triangle C is congruent to Triangle C’.
D. Triangle D’ is congruent to Triangle D.
C, D
Find the slope of each line.
(Karissa has pictures)
A. 1/2
B. 3
C. 2/3
A pool holds 19,900 gallons of water. There are two hoses that can be used to fill the pool, a large one and a small one. On an average day, it takes 5 hours to fill the pool with the large hose and 12 hours with the small hose. Create a graph to represent this scenario.
Karissa has the image
Solve this system of equations.
(1/2)x + 6y = 12
y = x +15
X = -12, y = 3
Describe a sequence of transformations that shows that Polygon A is congruent to Polygon B
(Karissa has image)
Answers vary. Sample solution: If Polygon A reflected across line l, a horizontal line 1 unit above the top of Polygon A, and then translated 3 units to the right, it matches up perfectly with Polygon B.
Triangles 1 and 2 are both isosceles. They each have a 30-degree angle. Explain why these triangles do not have to be similar to each other. If you get stuck, consider drawing a diagram.
They do not have to be similar because an isosceles triangle with only one 30-degree angle does not have the same angle measures as a triangle with two 30-degree angles.
A sandwich store charges a $10 delivery fee and $4.50 for each sandwich.
1. What is the total cost (sandwiches and delivery charge) if an office orders 6 sandwiches?
2. What is the total cost for X sandwiches?
3. Graph the total cost of sandwiches and delivery based on number of sandwiches ordered. Be sure to label your axes and scale them by labeling each gridline with a number.
1. $37
2. 10+4.5x
3. A line that passes through points (0,10), (1,14.5), and (2,19)
Lin and Han’s families provide money for their school lunch accounts. Han starts with $100 in his account. He spends $15 each week on lunches. Lin starts with $25 in her account and does not spend any of it. Her family adds $10 each week to her account.
At the end of 4 weeks, who has more money in their account?
Lin
For each pair of shapes, decide whether or not Shape A is congruent to Shape B. Explain your reasoning.
(Karissa has images)
1. Not congruent. The shapes look congruent, but when Shape A is moved on top of Shape B with a translation and a 90-degree clockwise rotation, they do not match up.
2. Congruent. If Shape A is translated so the upper right vertex coincides with the lower left vertex of B, reflected along the horizontal side of the image of Shape A, and then rotated 90 degrees clockwise around the upper right vertex, it will be placed on top of Shape B.
A line passes through points (5,13) and (2,4). What is the slope of the line?
3
A sandwich store charges a $10 delivery fee, and $4.50 for each sandwich.
4. Is there a proportional relationship between number of sandwiches and the cost of the order?
5. At a different sandwich shop, there is a $5 delivery fee, and each sandwich costs $4.50. On the same grid, graph the total cost of sandwiches and deliver based on number of sandwiches ordered for this new shop. Describe how the two graphs are the same and how they are different.
4. No
5. Possible responses: They have different vertical intercepts. They are parallel to each other. One is a translation of the other.
Lin and Han’s families provide money for their school lunch accounts. Han starts with $100 in his account. He spends $15 each week on lunches. Lin starts with $25 in her account and does not spend any of it. Her family adds $10 each week to her account.
After how many weeks will Han and Lin have the same amount of money in their lunch accounts?
3 weeks