Side-Side-Angle (Sometimes) Congruence

ID: mirof-duluj
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

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 ABCABC and triangle XYZXYZ:

  • Angle ABCABC and angle XYZXYZ are both 30°\degree
  • BCBC and YZYZ both measure 6 units
  • CACA and ZXZX 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 WYWY bisects angles ZWXZWX and ZYXZYX.

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4) Is she correct?

True or false? Write below.

5) Explain your reasoning.

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 CBECBE is congruent to angle DEADEA. \quad\quad b) Angle CEBCEB is congruent to angle DEADEA. \quad\quad c) Segment DADA is congruent to segment CBCB. \quad\quad d) Segment DCDC is congruent to segment ABAB. \quad\quad e) Line DCDC is parallel to line ABAB. \quad\quad f) Line DADA is parallel to line CDCD.

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Problem 5

7) WXYZWXYZ is a kite. Angle WXYWXY has a measure of 94 degrees and angle ZWXZWX has a measure of 112 degrees. Find the measure of angle ZYWZYW.

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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 ABAB such that ABAB is the perpendicular bisector of segment CDCD. We know angle ADBADB is congruent to 1 . DBDB is congruent to 2 since ABAB is the perpendicular bisector of CDCD. Angle 3 is congruent to angle 4 because they are both right angles. Triangle ABCABC is congruent to triangle 5 because of the 6 Triangle Congruence Theorem. ADAD is congruent to 7 because they are corresponding parts of congruent triangles. Therefore, triangle ADCADC 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: ACAC, ABDABD, ABCABC, CBCB, ACBACB, ASAASA

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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 DEFDEF onto triangle BACBAC?

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a) Translate DEF using directed line segment EA. Rotate DEF using A as the center so that D coincides with C Reflect DEF across line AC.\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) Translate DEF using directed line segment EA. Rotate DEF using A as the center so that D coincides with C Reflect DEF across line AB.\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) Translate DEF using directed line segment EA. Rotate DEF using A as the center so that D coincides with B Reflect DEF across line AC.\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) Translate DEF using directed line segment EA. Rotate DEF using A as the center so that D coincides with B Reflect DEF across line AB.\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{.}