Question

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.

Answer 1

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 _______1________.
ΔBAD is congruent to ΔBCD by the _______2________.
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.

Answer 2

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

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

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

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

Answer 3

please help??

Answer 4

@jhonyy9 plese help?

Answer 5

when is a triangle isoscele ?

Answer 6

when the two sides are equal

Answer 7

given <BAC congruent <ACB - yes ? so from this what result ?

Answer 8

would it be the second one?

Answer 9

so when 2 angles are congruent so from this result that the corresponding sides to these angles are congruent too - ok. ?

so than you check these angles from the base <BAC and <ACB are congruent by ,,GIVEN" from the start - so from this result that the coresponding sides to thses angles are congruent too - what are these sides ?

Answer 10

side BA and side BC - yes ?

Answer 11

coresponding angle A is side BC and coresponding angle C is BA - yes ?

Answer 12

so than BC congruent BA this mean that the triangle ABC is isoscele sure

Answer 13

ohh its the last one. @jhonyy9

Answer 14

are you sure ?

Answer 15

not really. @jhonyy9 sorry

Answer 16

but it uses asa

Answer 17

postulate

Answer 18

yes is right but you need to be sure when you are right - ok. ?

Answer 19

do u think its right? @jhonyy9

Answer 20

yes by ASA is sure correct

Answer 21

ohh okayy thank youuu

Answer 22

was my pleasure

bye bye