1) Painters and carpenters use scaffolding to climb buildings from the outside. What shapes do you see? Why does one figure have more right angles?
2) Select all true statements based on the diagram. Write each corresponding letter in the answer box and separate letters with commas.
a) Angle is congruent to angle . b) Angle is congruent to angle . c) Segment is congruent to segment . d) Segment is congruent to segment . e) Line is parallel to line . f) Line is parallel to line .
3) Prove is a parallelogram.
4) Tyler has proven that triangle is congruent to triangle using the Side-Side-Side Triangle Congruence Theorem. Why can he now conclude that diagonal bisects angles and ?
5) is a kite. Angle has a measure of 133 degrees and angle has a measure of 34 degrees. Find the measure of angle .
Elena is thinking through a proof using a reflection to show that the base angles of an isosceles triangle are congruent. Complete the missing information for her proof.
Call the midpoint of segment 1 . Construct the perpendicular bisector of segment . The perpendicular bisector of must go through since it's the midpoint. is also on the perpendicular of because the distance from to 2 is the same as the distance from to 3 . We want to show triangle is congruent to triangle . Reflect triangle across line 4 . Since 5 is on the line of reflection, it definitely lines up with itself. is congruent to 6 since is the perpendicular bisector of . will coincide with 7 since it is on the other side of a perpendicular line and the same distance from it (and that’s the definition of reflection!). will coincide with 8 since it is on the other side of a perpendicular line and the same distance from it (and that’s the definition of reflection!). Since the rigid transformation will take triangle onto triangle , that means angle 9 will be taken onto angle (they are corresponding parts under the same reflection), and therefore they are congruent.
Fill in the blanks using items from the Bank of Terms below. Some items might be used more than once.
Bank of Terms: , , , , , , ,
6) Blank 1
7) Blanks 2 and 3, answers separated by a comma.
8) Blank 4
9) Blank 5
10) Blank 6
11) Blank 7
12) Blank 8
13) Blanks 9 and 10, answers separated by a comma.
14) Segment is an angle bisector of angle . Noah wrote a proof to show that triangle is congruent to triangle . Noah's proof is not correct. Why is Noah's proof incorrect?
1. Side is congruent to side because they're the same segment.
2. Angle is congruent to angle because segment is an angle bisector of angle .
3. Angle is congruent to angle because segment is an angle bisector of angle .
4. By the Angle-Side-Angle Triangle Congruence Theorem, triangle is congruent to triangle .
15) Figure is the image of figure after being rotated 90 degrees counterclockwise around point . Draw an auxiliary line in figure to create a quadrilateral. Draw the image of the auxiliary line when rotated 90 degrees counterclockwise around point .
16) Write a congruence statement for the quadrilateral you created in figure and the image of the quadrilateral in figure .