Incenter and Circumcenter

Question 1

Is there a rigid transformation that maps triangle ABC to triangle ABD? If so, which transformation?

Revolt · Accepted Answer

yes, because a reflection across BA will map ΔABC to ΔABD

Question 2

We know that angle CBA is congruent to angle FBA and that angle CAB is congruent to angle FAB because . We see that is congruent to by the reflexive property of congruence. Therefore, we can conclude that triangle BCA is congruent to triangle BFA because .

Revolt · Accepted Answer

side BA

Question 3

We know that angle CBA is congruent to angle FBA and that angle CAB is congruent to angle FAB because . We see that is congruent to by the reflexive property of congruence. Therefore, we can conclude that triangle BCA is congruent to triangle BFA because .

Revolt · Accepted Answer

side BA

Question 4

We know that angle CBA is congruent to angle FBA and that angle CAB is congruent to angle FAB because . We see that is congruent to by the reflexive property of congruence. Therefore, we can conclude that triangle BCA is congruent to triangle BFA because .

Revolt · Accepted Answer

of ASA

Question 5

What additional information would be needed to prove that the triangles are congruent using the ASA congruence theorem?

Revolt · Accepted Answer

∠LNO ≅ ∠LNM

Question 6

Is there a rigid transformation that would map ΔABC to ΔDEC?

Revolt · Accepted Answer

yes, a rotation about point C

Question 7

We know that angle CBA is congruent to angle FBA and that angle CAB is congruent to angle FAB because . We see that is congruent to by the reflexive property of congruence. Therefore, we can conclude that triangle BCA is congruent to triangle BFA because .

Revolt · Accepted Answer

it is given

Incenter and Circumcenter Answers

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