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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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What are the coordinates of the endpoints A'B after a reflection of segment AB over the line y = - x?
kupik [55]

Answer:

by reflection, if you mean swapped, then the answers are A'(1,-6) and B'(4,2)

i hope these are the answers you are looking for

Step-by-step explanation:

6 0
3 years ago
Find the service area of a cylinder with a base diameter of 6ft and height of 4ft
tatiyna

The service area of the cylinder is 42\pi square fts.

<h3>What is cylinder?</h3>

Two parallel bases joined by a curving surface make up the three-dimensional solid known as a cylinder.

Typically, the bases are shaped like circles. The height "h" of the cylinder stands for the perpendicular distance between the bases, while "r" stands for the cylinder's radius.

The uses of cylinder are-

  • A popular piece of scientific equipment used to determine the volume of a liquid is a graduated cylinder, sometimes referred to as a measuring cylinder or mixing cylinder.
  • Its form is slender and cylindrical. The measured amount of liquid is shown by each marked line on the graduated cylinder.

Total surface area of the cylinder formula:

It is the sum of the base surface area and the lateral surface area;

Total area = base area + lateral area , or

Total area = 2 π r² + (2 π r) h , or

Total area = 2 π r (r + h)

Calculation for the total area of the cylinder;

Base diameter is 6 ft

Radius is 6/2 = 3 ft

Height is 4 ft

Total area = 2\pi3(3 + 4)

                 = 6\pi×7

                 = 42\pi

Therefore, the total surface area of the cylinder is 42\pi square fts.

To know more about the surface area of the cylinder, here

brainly.com/question/10332927

#SPJ4

5 0
2 years ago
Sam ran 40 yards in 5 seconds. What was her rate of speed in miles per hour? A) 2 mph B) 5 mph C) 16 mph D) 22 mph
SVEN [57.7K]

B) 5 mph

hope this helped

6 0
3 years ago
Read 2 more answers
Can someone pls find the slope and y-intercept ASAP!!
Semenov [28]

Answer:

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3 0
3 years ago
F(x) = x ^ 2 - 8x + 7
bekas [8.4K]
Answer:
They have the same x-value
f(x) has the greater minimum
Step-by-step explanation:
To find the vertex of a second degree equation, in this case the minimum value, we can use the following equation:
x = -b / 2a
Remember that a second degree equation has the following form:
ax^2 + bx + c
so a = 1, b = -8 and c = 7. Now you have to substitute in the previous equation
x = - (-8) / 2(1)
x = 8 / 2
x = 4
This means that the two functions have the same x-value.
The y value of f(x) would be
f(4) = (4)^2 - 8(4) + 7
f(4) = 16 - 32 + 7
f(4) = -9
So the vertex, or minimun value of f(x) would be at the point (4, -9).
The vertex, or minimun value of g(x) is at the point (4, -4).
So f(x) has a minimum value of -9 and g(x) a minimum value of -4.
5 0
3 years ago
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