Question

In ΔABC shown below, ∠BAC is congruent to ∠BCA.

Answer 1

Given: Base ∠BAC and ∠ACB are congruent.

Prove: ΔABC is an isosceles triangle.

When completed (fill in the blanks), the following paragraph proves that Line segment AB is congruent to Line segment BC making ΔABC an isosceles triangle.

Construct a perpendicular bisector from point B to Line segment AC.
Label the point of intersection between this perpendicular bisector and Line segment AC as point D.
m∠BDA and m∠BDC is 90° by the definition of a perpendicular bisector.
∠BDA is congruent to ∠BDC by the _______1________.
Line segment AD is congruent to Line segment DC by _______2________.
ΔBAD is congruent to ΔBCD by the Angle-Side-Angle (ASA) Postulate.
Line segment AB is congruent to Line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).
Consequently, ΔABC is isosceles by definition of an isosceles triangle.

the definition of congruent angles
Angle-Side-Angle (ASA) Postulate

the definition of congruent angles
the definition of a perpendicular bisector

Angle-Side-Angle (ASA) Postulate
the definition of a perpendicular bisector

Angle-Side-Angle (ASA) Postulate
corresponding parts of congruent triangles are congruent (CPCTC)

Answer 2

@RaphaelFilgueiras Help on math

Answer 3

@BellaNina865 Math Help

Answer 4

@jigglypuff314 Help on one more

Answer 5

ASA is for proving that two triangles are congruent.
neither 1 nor 2 mention triangles

Answer 6

as in, which option does not mention ASA?

Answer 7

B

Answer 8

the second one

Answer 9

That's what I got :)

Answer 10

the definition of congruent angles
the definition of a perpendicular bisector