# Side-Side-Angle (Sometimes) Congruence

ID: mirof-duluj Illustrative Math
Subject: Geometry

# Side-Side-Angle (Sometimes) Congruence

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##### Problem 1

1) Which of the following criteria always proves triangles congruent? Select all that apply. Write each corresponding letter in the answer box and separate letters with commas.

a) 3 congruent angles ﻿$\quad\quad$﻿ b) 3 congruent sides ﻿$\quad\quad$﻿ c) Corresponding congruent Side-Angle-Side ﻿$\quad\quad$﻿ d) Corresponding congruent Side-Side-Angle ﻿$\quad\quad$﻿ e) Corresponding congruent Angle-Side-Angle

##### Problem 2

2) Here are some measurements for triangle ﻿$ABC$﻿ and triangle ﻿$XYZ$﻿:

• Angle ﻿$ABC$﻿ and angle ﻿$XYZ$﻿ are both 30﻿$\degree$﻿
• ﻿$BC$﻿ 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.

3) Explain why triangles with 3 congruent parts aren't necessarily congruent.

##### Problem 3

Jada states that diagonal ﻿$WY$﻿ bisects angles ﻿$ZWX$﻿ and ﻿$ZYX$﻿. 4) Is she correct?

True or false? Write below.

##### Problem 4

6) Select all true statements based on the diagram. Write each corresponding letter in the answer box and separate letters with commas.

a) Angle ﻿$CBE$﻿ is congruent to angle ﻿$DEA$﻿. ﻿$\quad\quad$﻿ b) Angle ﻿$CEB$﻿ is congruent to angle ﻿$DEA$﻿. ﻿$\quad\quad$﻿ c) Segment ﻿$DA$﻿ is congruent to segment ﻿$CB$﻿. ﻿$\quad\quad$﻿ d) Segment ﻿$DC$﻿ is congruent to segment ﻿$AB$﻿. ﻿$\quad\quad$﻿ e) Line ﻿$DC$﻿ is parallel to line ﻿$AB$﻿. ﻿$\quad\quad$﻿ f) Line ﻿$DA$﻿ is parallel to line ﻿$CD$﻿. ##### Problem 5

7) ﻿$WXYZ$﻿ 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 ﻿$ZYW$﻿. ##### 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 1 . ﻿$DB$﻿ is congruent to 2 since ﻿$AB$﻿ is the perpendicular bisector of ﻿$CD$﻿. Angle 3 is congruent to angle 4 because they are both right angles. Triangle ﻿$ABC$﻿ is congruent to triangle 5 because of the 6 Triangle Congruence Theorem. ﻿$AD$﻿ is congruent to 7 because they are corresponding parts of congruent triangles. Therefore, triangle ﻿$ADC$﻿ is an isosceles triangle.

Fill in the blanks using items from the Bank of Terms below. Some items might be used more than once.

Bank of Terms: ﻿$AC$﻿, ﻿$ABD$﻿, ﻿$ABC$﻿, ﻿$CB$﻿, ﻿$ACB$﻿, ﻿$ASA$﻿ 8) Blank 1

9) Blank 2

10) Blanks 3 and 4, answers separated by a comma.

11) Blank 5

12) Blank 6

13) Blank 7

##### Problem 7

14) The triangles are congruent. Which sequence of rigid motions takes triangle ﻿$DEF$﻿ onto triangle ﻿$BAC$﻿? a) $\text{Translate } DEF \text{ using directed line segment } EA \text{. Rotate } D'E'F' \text{ using } A \text{ as the center so that } D' \text{ coincides with } C \text{. } \newline \text{ Reflect } D''E''F'' \text{ across line } AC \text{.}$b) $\text{Translate } DEF \text{ using directed line segment } EA \text{. Rotate } D'E'F' \text{ using } A \text{ as the center so that } D' \text{ coincides with } C \text{. } \newline \text{ Reflect } D''E''F'' \text{ across line } AB \text{.}$c) $\text{Translate } DEF \text{ using directed line segment } EA \text{. Rotate } D'E'F' \text{ using } A \text{ as the center so that } D' \text{ coincides with } B \text{. } \newline \text{ Reflect } D''E''F'' \text{ across line } AC \text{.}$d) $\text{Translate } DEF \text{ using directed line segment } EA \text{. Rotate } D'E'F' \text{ using } A \text{ as the center so that } D' \text{ coincides with } B \text{. } \newline \text{ Reflect } D''E''F'' \text{ across line } AB \text{.}$