Lesson 11

Side-Side-Angle (Sometimes) Congruence

Problem 1

Which of the following criteria always proves triangles congruent? Select all that apply.

A:

3 congruent angles

B:

3 congruent sides

C:

Corresponding congruent Side-Angle-Side

D:

Corresponding congruent Side-Side-Angle

E:

Corresponding congruent Angle-Side-Angle

Problem 2

Here are some measurements for triangle $$\ ABC$$ and triangle $$XYZ$$:

• Angle $$ABC$$ and angle $$XYZ$$ are both 30°
• $$BC$$ and $$YZ$$ both measure 6 units
• $$CA$$ and $$ZX$$ both measure 4 units

Lin thinks thinks these triangles must be congruent. Priya says she knows they might not be congruent. Construct 2 triangles with the given measurements that aren't congruent. Explain why triangles with 3 congruent parts aren't necessarily congruent.

Problem 3

Jada states that diagonal $$WY$$ bisects angles $$ZWX$$ and $$ZYX$$. Is she correct? Explain your reasoning,

Solution

(From Unit 2, Lesson 9.)

Problem 4

Select all true statements based on the diagram.

A:

Angle $$CBE$$ is congruent to angle $$DAE$$.

B:

Angle $$CEB$$ is congruent to angle $$DEA$$.

C:

Segment $$DA$$ is congruent to segment $$CB$$.

D:

Segment $$DC$$ is congruent to segment $$AB$$.

E:

Line $$DC$$ is parallel to line $$AB$$.

F:

Line $$DA$$ is parallel to line $$CB$$.

Solution

(From Unit 2, Lesson 10.)

Problem 5

$$WXYZ$$ is a kite. Angle $$WXY$$ has a measure of 94 degrees and angle $$ZWX$$ has a measure of 112 degrees. Find the measure of angle $$ZYW$$.

Solution

(From Unit 2, Lesson 9.)

Problem 6

Andre is thinking through a proof using a reflection to show that a triangle is isosceles given that its base angles are congruent. Complete the missing information for his proof.

Construct $$AB$$ such that $$AB$$ is the perpendicular bisector of segment $$CD$$. We know angle $$ADB$$ is congruent to $$\underline{\hspace{.5in}1\hspace{.5in}}$$$$DB$$ is congruent to $$\underline{\hspace{.5in}2\hspace{.5in}}$$ since $$AB$$ is the perpendicular bisector of $$CD$$.  Angle $$\underline{\hspace{.5in}3\hspace{.5in}}$$ is congruent to angle $$\underline{\hspace{.5in}4\hspace{.5in}}$$ because they are both right angles. Triangle $$ABC$$ is congruent to triangle $$\underline{\hspace{.5in}5\hspace{.5in}}$$ because of the $$\underline{\hspace{.5in}6\hspace{.5in}}$$ Triangle Congruence Theorem. $$AD$$ is congruent to $$\underline{\hspace{.5in}7\hspace{.5in}}$$ because they are corresponding parts of congruent triangles. Therefore, triangle $$ADC$$ is an isosceles triangle.

Solution

(From Unit 2, Lesson 8.)

Problem 7

The triangles are congruent. Which sequence of rigid motions takes triangle $$DEF$$ onto triangle $$BAC$$?

A:

Translate $$DEF$$ using directed line segment $$EA$$. Rotate $$D’E’F’$$ using $$A$$ as the center so that $$D’$$ coincides with $$C$$. Reflect $$D’’E’’F’’$$ across line $$AC$$.

B:

Translate $$DEF$$ using directed line segment $$EA$$. Rotate $$D’E’F’$$ using $$A$$ as the center so that $$D’$$ coincides with $$C$$. Reflect $$D’’E’’F’’$$ across line $$AB$$.

C:

Translate $$DEF$$ using directed line segment $$EA$$. Rotate $$D’E’F’$$ using $$A$$ as the center so that $$D’$$ coincides with $$B$$. Reflect $$D’’E’’F’’$$ across line $$AC$$.

D:

Translate $$DEF$$ using directed line segment $$EA$$. Rotate $$D’E’F’$$ using $$A$$ as the center so that $$D’$$ coincides with $$B$$. Reflect $$D’’E’’F’’$$ across line $$AB$$.