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Triangle Congruence: ASA and AAS (100%)
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During geometry class, students are told that ΔTSR ≅ ΔUSV. Marcus states that ΔTSR is mapped to ΔUSV by performing a rotation about point S. Sam states that ΔTSR is mapped to ΔUSV by a reflection across the line that goes through point S. Determine if either student is correct.
A. Marcus is correct.
Are the triangles congruent? If so, how do you know?
C. yes, because of ASA or AAS
Explain how the angle-angle-side congruence theorem is an extension of the angle-side-angle congruence theorem. Be sure to discuss the information you would need for each theorem.
The interior angles measures of a triangle add up to 180 degrees. Thus, if you are given angle-angle-side, you can solve for the third angle measures and essentially have angle-side-angle because the given side will now be the included side.
Given: ≅
≅
Prove: ≅
It is given that angle LNO is congruent to angle and angle OLN is congruent to angle . We know that side LN is congruent to side LN because of the . Therefore, because of , we can state that triangle LNO is congruent to triangle LNM.
LNM, MLN, reflexive property, ASA
Isabelle proves that the triangles are congruent by using the parallel lines to determine a second set of angles are congruent. What statement and reason could she have used?
C. ∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent
Determine the rigid transformations that will map ΔABC to ΔXYZ.
D. Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
Which shows two triangles that are congruent by AAS?
A
What additional information is needed to prove that the triangles are congruent using the ASA congruence theorem?
D. L ≅ P
What additional information could be used to prove that the triangles are congruent using AAS or ASA? Check all that apply.
A. <B ~= <P and BC ~= PQ
B. <A ~= <T and AC = TQ = 3.2cm
D. <A ~= <T and BC ~= PQ
Two rigid transformations are used to map JKL to MNQ. The first is a translation of vertex L to vertex Q. What is the second transformation?
C. a rotation about point L
Given: ABC and FGH are right angles; BA||GF; BC ≅ GH
Prove: ABC ≅ FGH
Step 1: We know that ABC ≅ FGH because all right angles are congruent.
Step 2: We know that BAC ≅ GFH because corresponding angles of parallel lines are congruent.
Step 3: We know that BC ≅ GH because it is given.
Step 4: ABC ≅ FGH because of the
B. AAS congruence theorem
Which rigid transformation would map MZK to QZK?
C. a reflection across the line containing ZK
Which of these triangle pairs can be mapped to each other using two reflections?
A.
What additional information could be used to prove that the triangles are congruent using AAS? Check all that apply.
B. CB ≅ QM
C. AC = 3.9cm and RQ = 3.9cm
Can a translation and a reflection map QRS to TUV? Explain why or why not.
B. Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map.
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