Congruent Parts, Part 2
Line is a line of symmetry for figure . Noah says that is congruent to because sides and are corresponding.
1) Why is Noah’s congruence statement incorrect?
2) What pentagon is congruent to pentagon ?
Figure is the image of figure after being rotated 90 degrees counterclockwise about point .
3) Draw a segment in figure to create a quadrilateral.
4) Draw the image of the segment when rotated 90 degrees counterclockwise about point .
5) Write a congruence statement for the quadrilateral you created in figure and the image of the quadrilateral in figure .
6) Triangle is the image of triangle after a 180 degree rotation about point .
Select statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.
a) Triangle is congruent to triangle . b) Triangle is congruent to triangle . c) Angle is congruent to angle . d) Angle is congruent to angle . e) Segment is congruent to segment . f) Segment is congruent to segment .
7) When triangle is reflected across line , the image is triangle . Why are segment and segment congruent?
Congruent parts of congruent figures are corresponding.
Corresponding parts of congruent figures are congruent.
An isosceles triangle has a pair of congruent sides.
Segment is a perpendicular bisector of segment .
Elena needs to prove angles and are congruent. Provide reasons to support each of her statements.
8) Line is parallel to line .
9) Angles and are congruent.
10) Triangle is the image of isosceles triangle after a reflection across line . Select the statements that are a result of corresponding parts of congruent triangles being congruent. Write each corresponding letter in the answer box and separate letters with commas.
a) is a rectangle. b) is a rhombus. c) Diagonal bisects angles and . d) Diagonal is perpendicular to side . e) Angle is congruent to angle . f) Angle is congruent to angle .
This design began from the construction of a regular hexagon.
11) Draw 1 segment so the diagram has another hexagon that is congruent to hexagon .
12) Explain why the hexagons are congruent.