Lesson 5

Points, Segments, and Zigzags

  • Let’s figure out when segments are congruent.

Problem 1

Write a sequence of rigid motions to take figure \(ABC\) to figure \(DEF\).

Two figures, A B C and D E F.

Problem 2

Prove the circle centered at \(A\) is congruent to the circle centered at \(C\).

\(AB=CD\)

Two circles. First circle, center A, with point B on circle. Radius A B drawn. Second circle, center C, with point D on circle. Radius C D drawn. A B and C D have one tick mark showing congruence.

Problem 3

Which conjecture is possible to prove?

A:

All quadrilaterals with at least one side length of 3 are congruent.

B:

All rectangles with at least one side length of 3 are congruent.

C:

All rhombuses with at least one side length of 3 are congruent.

D:

All squares with at least one side length of 3 are congruent.

Problem 4

Match each statement using only the information shown in the pairs of congruent triangles.

A:

The 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle.

B:

The 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle.

C:

In the 2 triangles there are 3 pairs of congruent sides.

1:
Two congruent triangles. On each triangle, an angle marked with two tick marks, a side marked with one tick mark, and an angle marked with one tick mark.
2:
2 triangles, with 3 corresponding, congruent sides, with tic marks. Diagonal is marked with one tic mark, shorter bottom side is marked by 2 tic marks, longer side is marked by 3 tic marks.
3:
Two congruent triangles. On each triangle, the long diagonal is marked with 1 tic mark, the bottom short side is marked with 2 tic marks, and the angle between the 2 sides is marked with 1 tic mark.  
(From Unit 2, Lesson 4.)

Problem 5

Triangle \(HEF\) is the image of triangle \(HGF\) after a reflection across line \(FH\). Write a congruence statement for the 2 congruent triangles.

Triangle  H E F is the image of triangle  H G F.
(From Unit 2, Lesson 2.)

Problem 6

Triangle \(ABC\) is congruent to triangle \(EDF\). So, Lin knows that there is a sequence of rigid motions that takes \(ABC\) to \(EDF\).  

Select all true statements after the transformations:

Triangle ABC is congruent to triangle EDF.
A:

Angle \(A\) coincides with angle \(F\).

B:

Angle \(B\) coincides with angle \(D\).

C:

Angle \(C\) coincides with angle \(E\).

D:

Segment \(BA\) coincides with segment \(DE\).

E:

Segment \(BC\) coincides with segment \(FE\).

(From Unit 2, Lesson 3.)

Problem 7

This design began from the construction of a regular hexagon. Is quadrilateral \(JKLO\) congruent to the other 2 quadrilaterals? Explain how you know.

2 Hexagons and quadrilaterals.
(From Unit 1, Lesson 22.)