In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent 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. (4 points) 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 line segment ab is congruent to line segment bc because 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)

1. Angle-Side-Angle (ASA) Postulate

2. Corresponding parts of congruent triangles are congruent (CPCTC)

Step-by-step explanation:

Given : ABC is a triangle,

In which, ∠BAC ≅ ∠BCA

To prove : Δ ABC is an isosceles triangle,

Proof:

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

∠BAC ≅ ∠BCA                   ( Given )

Since, ∠BDA ≅ ∠BDC       ( Right angles )

AD ≅ DC               (By the definition of a perpendicular bisector. )

Thus, By ASA postulate of congruence,

Δ BAD ≅ Δ BCD

⇒ AB ≅ BC ( By CPCTC )

⇒ ΔABC is isosceles ( by definition of an isosceles triangle )

-4

step-by-step explanation:

do 6-10=

if u need it to be negative.

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.