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Georgia Department of Education
Common Core Georgia Performance Standards Framework Teacher Edition
Analytic Geometry • Unit 1
Proving Two Triangles are Congruent
Mathematical Goals
• Knowing that rigid transformations preserve size and shape or distance and angle, use this
fact to connect the idea of congruency and develop the definition of congruent.
• Use the definition of congruence, based on rigid motion, to show two triangles are congruent
if and only if their corresponding sides and corresponding angles are congruent.
• Use the definition of congruence, based on rigid motion, to develop and explain the triangle
congruence criteria; ASA, SSS, and SAS, AAS.
STANDARDS ADDRESSED IN THIS TASK
MCC9-12.G.CO.6 Use geometric descriptions of rigid motions to transform figures and to
predict the effect of a given rigid motion on a given figure; given two figures, use the definition
of congruence in terms of rigid motions to decide if they are congruent.
MCC9-12.G.CO.7 Use the definition of congruence in terms of rigid motions to show that two
triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of
angles are congruent.
MCC9-12.G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS)
follow from the definition of congruence in terms of rigid motions.
Standards for Mathematical Practice
4. Model with mathematics by expecting students to apply the mathematics concepts
they know in order to solve problems arising in everyday situations, and reflect on
whether the results are sensible for the given scenario.
5. Use appropriate tools strategically by expecting students to consider available tools
when solving a mathematical problem. These tools might include pencil and paper,
concrete models, a ruler, a protractor, a compass, a calculator, software, etc.
6. Attend to precision by requiring students to calculate efficiently and accurately; and
to communicate precisely with others by using clear mathematical language to discuss
their reasoning.
7. Look for and make use of structure by expecting students to apply rules, look for
patterns and analyze structure.
8. Look for and express regularity in repeated reasoning by expecting students to
understand broader applications and look for structure and general methods in similar
situations.
MATHEMATICS  ANALYTIC GEOMETRY  UNIT 1: Similarity, Congruence, and Proofs
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2013 • Page 118 of 188
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework Teacher Edition
Analytic Geometry • Unit 1
Triangle Investigations: Station 1
1. Draw a triangle of any size and shape and label it ABC.
2. Using the ruler and protractor, measure and record the angles and sides of the triangle.
Remember the total degrees in any triangle should be _______?
3. Draw ∆DOG where AB=DO, BC=OG, and AC=DG.
4. Measure and record the angles of ∆ DOG, how are they related to the angles of ABC?
5. Do you have enough information to conclude that ∆ABC and ∆DOG are congruent?
Why or why not?
Triangle Investigations: Station 2
1. Draw ∆ KIT where KI=5 cm.
2. Using a protractor and point K as a vertex draw a 60o angle with side length 11cm (label
point T).
3. Connect point T to point I.
4. Measure the sides and angles of ∆ KIT.
5. Now draw a line segment of 11cm. Name it FG.
6. Using point F as your vertex draw a 60o angle with side length 5 cm. label point H.
7. Connect point G to point H.
8. Measure the sides and angles of ∆ FGH.
9. Are triangles KIT and FGH congruent? Why or why not?
Triangle Investigations: Station 3
1.
2.
3.
4.
Draw a line segment that is 7cm long. Label it ML.
Using point L as a vertex draw a 38o angle.
Draw a line segment beginning at point M that is 5 cm long and hits the side of the angle?
Repeat steps 1-2. This time connect the 5 cm segment at a different point on the side of
the angle.
5. Are the 2 triangles congruent? Why or why not?
Triangle Investigations: Station 4
1.
2.
3.
4.
5.
6.
Draw a line segment LM that is 7 inches long.
Using point L as a vertex draw a 35o angle.
Using point M as a vertex draw a 57o angle.
Label the point of intersection of the two angles as N. This is triangle LMN.
Draw line segment ST that is 7 inches long.
Using point S as a vertex draw a 35o angle.
MATHEMATICS  ANALYTIC GEOMETRY  UNIT 1: Similarity, Congruence, and Proofs
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2013 • Page 119 of 188
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework Teacher Edition
Analytic Geometry • Unit 1
7. Using point T as a vertex draw a 57o angle.
8. Label the point of intersection of the two angles as U. This is triangle STU
9. Hold up the two triangles - are they congruent? Why or why not?
MATHEMATICS  ANALYTIC GEOMETRY  UNIT 1: Similarity, Congruence, and Proofs
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2013 • Page 120 of 188
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework Teacher Edition
Analytic Geometry • Unit 1
Triangle Investigations: Station 5
Practice with Triangle Congruence
State whether each pair of triangles is congruent by SSS, SAS, ASA, AAS, or HL; if none of
these methods work, write N. If congruent, make a congruence statement for the triangles.
U
H
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B
MATHEMATICS  ANALYTIC GEOMETRY  UNIT 1: Similarity, Congruence, and Proofs
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2013 • Page 121 of 188
All Rights Reserved
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