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Verdich [7]
3 years ago
11

Given: ΔABC, where AB = BC Prove: m∠BAC = m∠BCA Statement Reason 1. Let ΔABC be an isosceles triangle with AB = BC. given 2. Cre

ate point D on side so bisects ∠ABC. constructing an angle bisector 3. M∠ABD = m∠CBD definition of angle bisector 4. BD = BD Reflexive Property of Equality 5. ΔABD ≅ ΔCBD 6. M∠BAC = m∠BCA Corresponding angles of congruent triangles have equal measures. What is the reason for statement 5 in this proof? A. ASA B. SSS C. AAS D. SAS
Mathematics
1 answer:
weqwewe [10]3 years ago
4 0

Answer:

D. SAS

Step-by-step explanation:

Given: ΔABC

Bisecting <ABC to create point D implies that BD is a common side to  ΔABD and ΔCBD.

Also,

m<ABD = m<CBD (angle bisector)

BA = BC (given property of the isosceles triangle)

Therefore,

ΔABD ≅ ΔCBD (Side Angle Side)

The reason for statement 5 in this proof is that ΔABD ≅ ΔCBD by SAS (Side-Angle-Side) relations of the congruent triangles.

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The domain of the function is a (-∞, 0) and the range of the function will be f(x) < 0. Then the correct option is C.

<h3>What are domain and range?</h3>

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

f(x) = 2x – 41

Then the domain of the function is a (-∞, 0) and the range of the function will be f(x) < 0.

Then the correct option is C.

More about the domain and range link is given below.

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If B is the midpoint of AC, then |AB| = |AC|.
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