Question

Math help please! WILL MEADL!!

Answer 1

In ΔABC shown below, ∠BAC is congruent to ∠BCA:
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 definition of congruent angles.
Line segment AD is congruent to Line segment DC by by the definition of a perpendicular bisector.

ΔBAD is congruent to ΔBCD by the _______1________.
Line segment AB is congruent to Line segment BC because _______2________.
Consequently, ΔABC is isosceles by definition of an isosceles triangle.

1.corresponding parts of congruent triangles are congruent (CPCTC)
2.the definition of a perpendicular bisector

1.the definition of a perpendicular bisector
2.the definition of congruent angles

1.the definition of congruent angles
2.the definition of a perpendicular bisector

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

Answer 2

as ∠BAC is congruent to ∠BCA,

the sides opposite to these angles are equal, that is BC and AB, In an isosceles triangle two sides are equal.

Answer 3

which option would it be then?

Answer 4

@Ashleyisakitty @Hero

Answer 5

I am confused. help me not be

Answer 6

to be honest, just knowing the two angles are the same is enough, but let's see

Answer 7

these are the options
1.corresponding parts of congruent triangles are congruent (CPCTC)
2.the definition of a perpendicular bisector

1.the definition of a perpendicular bisector
2.the definition of congruent angles

1.the definition of congruent angles
2.the definition of a perpendicular bisector

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

Answer 8

alright, so draw what they are doing in a picture so we can follow their method

Answer 9

hint, this is essentially the same as the last problem we worked on

Answer 10

would it the last option?

Answer 11

that would be my choice