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Triangle Congruence: ASA and AAS Assignment and Quiz
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Terms in this set (19)
What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.
∠Z ≅ ∠G and XZ ≅ FG
∠Z ≅ ∠G and XY ≅ FE
Can you conclude that triangle GHF is congruent to triangle GJK? Explain.
not enough information given
If two triangles have three congruent, corresponding angles, what additional information is needed to prove that the triangles are congruent?
To prove that two triangles with three congruent, corresponding angles are congruent, you would need to have at least one set of corresponding sides that are also congruent. You could then use ASA or AAS congruence theorems or rigid transformations to prove congruence.
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.
Marcus is correct.
Are the triangles congruent? If so, how do you know?
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 angle measures of a triangle add up to 180 degrees. Thus, if you are given angle-angle-side, you can solve for the third angle measure and essentially have angle-side-angle because the given side will now be the included side.
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
Given: AB || DC
∠A ≅ ∠D
Prove: ΔABC ≅ ΔDCB
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?
∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent
Determine the rigid transformations that will map ΔABC to ΔXYZ.
Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?
D
What additional information could be used to prove that the triangles are congruent using AAS or ASA? Check all that apply.
B ≅ P and BC ≅ PQ
A ≅ T and AC = TQ = 3.2cm
A ≅ T and BC ≅ PQ
Which of these triangle pairs can be mapped to each other using a reflection and a translation?
B
Which shows two triangles that are congruent by ASA?
B
Can a translation and a reflection map QRS to TUV? Explain why or why not.
Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map
△QRS to △TUV.
Which rigid transformation would map MZK to QZK?
a reflection across the line containing ZK
Given: TSR and QRS are right angles; T ≅ Q
Prove: TSR ≅ QRS
Step 1: We know that TSR ≅ QRS because all right angles are congruent.
Step 2: We know that T ≅ Q because it is given.
Step 3: We know that SR ≅ RS because of the reflexive property.
Step 4: TSR ≅ QRS because
of the AAS congruence theorem
Which of these triangle pairs can be mapped to each other using two reflections?
A
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?
a rotation about point L
Which statements are true about additional information for proving that the triangles are congruent? Check all that apply.
If A ≅ T, then the triangles would be congruent by ASA.
If B ≅ P, then the triangles would be congruent by AAS.
Related questions
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the measurement of the length between two points
QUESTION
inductive reasoning moves from specific instances into a generalized conclusion, while deductive reasoning moves from generalized principles that are known to be true to a true and specific conclusion. The accuracy of inductive reasoning is questionable.
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