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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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5 0
2 years ago
You need to buy 5 notebooks for your classes at school.Each notebook costs $2.79. What is the total cost before tax?
lesya692 [45]

Answer:

$13.95

Step-by-step explanation:

You need to multiply the 5 notebooks with the costs of each notebook, which gives you the total costs before tax.

7 0
3 years ago
In a right triangle, one leg is 20 cm and the hypotenuse is 30 cm. To the nearest hundredth of a cm, find the length of the miss
max2010maxim [7]

Answer:

Step-by-step explanation:

Use Pythagoras’ theorem

square of hypotenuse = sum of squares of two other sides

let the missing side be d

30^2 = 20^2 + d^2

600 = 400 + d^2

d^2 = 200

d = square root of 200

d = 14.142 cm

3 0
3 years ago
Read 2 more answers
GIVING BRAINILEST-
Nutka1998 [239]

Answer:

To construct a dilation, we need the center of dilation, which is the point from which we make the image smaller or larger. We also need a scale factor, which is the number that determines how large or small we are making the new image. If the scale factor is greater than 1, we have an enlargement, because the new image will be larger than the original image. If the scale factor is less than 1, we have a reduction because the new image will be smaller than the original image.

Enlargement

Step-1

Let's dilate triangle PQR by a scale factor of 2 with a center of dilation at point C.

Step-2

First, we will use a straightedge to connect the center of dilation C to each vertex. We are going to extend those lines across the whole page.

Step-3

Next, we'll place the point of the compass on the center of dilation C and the pencil on vertex Q and measure that distance.

Step-4

Now, without changing the size of the compass, we will move the point of the compass to vertex Q, and make a mark on the line that is extended through Q.

Step-5

Notice that since we measured the distance from C to Q and then used that same distance to mark the line, we have now created a new point that is twice the distance from C that Q was.

We now repeat the process for each of the other vertices of the triangle.

Step-6

These marks represent the vertices of our dilated image. We often use the same letters with an apostrophe to show that it is the corresponding vertex.

Step-7

Finally, we use the straightedge to connect all of the new vertices.

Now,See how triangle P

′

Q

′

R

′

is twice the size of the original triangle.

Reduction

Step-1

Given triangle PQR, now let's dilate the image with a center of dilation at C and with a scale factor of

2

1

Step-2

Using the straightedge, we will connect all of the vertices to the center of dilation C. In this case, since our scale factor is less than 1, we are reducing the size of the triangle.

Step-3

The green lines are the new lines that we have drawn.

Since we have to reduce the size of the triangle by half, we want to cut the distance in half from each vertex to the center of dilation. In order to do this, we will set our compass to a distance that is more than halfway between vertex P and point C but less than the total distance.

Step-4

Keeping the compass at that same distance, start with the point of the compass on vertex P, then draw a curve that intersects the line between P and C. Next, keeping the compass at the same distance, place the point of the compass on C and draw a curve that intersects the line between P and C and intersects the previously drawn curve.

Step-5

Now, we will take the straightedge and connect the points where the curves overlap.

4 0
2 years ago
PLEASE HELP ME I NEED TO PAST THIS TEST. Jack invests $30,000 with an interest rate of 4.5% compounded quarterly. After 6 years,
zavuch27 [327]

Answer:

1350

Step-by-step explanation:

Hope this helps!

3 0
3 years ago
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