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1 year ago

A student is given this proof.

Mathematics

1 answer:

Alenkasestr [34]1 year ago

5 0

From the steps below, it has been proved that by transitive property of congruence, we can say that; ∠CON ≅ ∠BOM

<h3>How to prove congruent angles?</h3>

We are given;

∠AOM ≅ ∠DON

To prove that;

∠CON ≅ ∠BOM

Now, from the image attached, we can say that;

∠BOM ≅ ∠DON because of vertical angles theorem

Similarly, we can say that ∠AOM ≅ ∠BOM due to transitive property of congruence.

Also, we can say that from vertical angles theorem, ∠AOM ≅ ∠CON

Finally, since ∠AOM ≅ ∠BOM, then by transitive property of congruence, we can say that;∠CON ≅ ∠BOM

Read more about Congruent Angles at; brainly.com/question/3168048

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A company that makes hair-care products had 4,000 people try a new shampoo. Of the 4,000 people, 28 had a mild allergic reacti

lyudmila [28]

Answer:

0.007%

Step-by-step explanation:

4000/28=0.007%

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3 years ago

the 43rd term of an arithmetic sequence is -671 and the 52nd term is -806. find the first term and the common difference.

Bond [772]

Answer:

First term = -41.

Common difference = -15.

Step-by-step explanation:

nth term: an = a1 + (n - 1)d where a = first term and d = the common difference.

-671 = a1 + (43 - 1)d

-806 = a1 +(52 - 1)d

-671 = a1 + 42d

-806 = a1 + 51d

Subtracting ( to eliminate a1):

-671 - (-806) = 42d - 51d

-9d = 135

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Substitute for d in the first equation:

-671 = a1 + 42*-15

-671 = a1 - 630

a1 = -671 + 630 = -41.

3 0

2 years ago

Joelle is working on a school report in a word processor. She wants to place an oversized image which is 30.51 \text{ cm}30.51 c

ehidna [41]

Answer:

the horizontal position for the left edge of the image is -4.46 cm.

Step-by-step explanation:

The horizontal midpoint of the page is:

21.59 / 2 = 10.79 cm

The horizontal midpoint of the image is given as:

30.51 / 2 = 15.25 cm

These midpoints must be on the same point in the axis.

By taking the leftmost edge of the paper to be point zero on the axis, then, the distance accommodated by the paper is 10.795 cm.

The distance that goes beyond this leftmost edge is computed as;

This is on the negative side on the axis.

Thus the horizontal position for the left edge of the image is -4.46 cm.

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3 years ago

Perimeter of a square that measures 5.35 cm on one side

Kitty [74]

Answer:

Perimeter of a square that measure 5.35 on one side is, 21.4 cm

Step-by-step explanation:

Perimeter of a square is the total length of the boundary of a square.

It is given by:

$P = 4a$ ......[1] where

P represents the perimeter of square,

a represents the side of square.

Given: a = 5.35 cm

Substitute this value in [1] we get;

P = 4(5.35) = 21.4 cm

therefore, the perimeter of a square is, 21.4 cm

6 0

3 years ago

What congruence rule does the triangle follow? Please write the congruence statement triangle EFH is congruent to ________?

Yuliya22 [10]

We can see here two triangles, and we can notice the following:

1. Since H is the midpoint of the segment EG, we can say that EH and HG are congruent segments.

2. Since these two triangles, namely, EFH and GFH share the same segment (HF), this side is also congruent to these two triangles.

3. Since EH is congruent to HG, and FH is congruent to itself, then EF is congruent to GF.

4. Angle E is congruent to angle G.

Therefore, we can say that:

Since we have that:

a. EF is congruent to GF

b. EH is congruent to GH

c. Angle E is congruent to angle G

We can conclude that the congruence rule, in this case, is SAS (Side-Angle-Side), because<em> if two sides and the included angle are congruent to the corresponding parts of the other triangle, the triangles are congruent.</em>

<em>We also see that the three sides are congruent (and in this case, we can also conclude that the triangles are congruent by the rule SSS (side-side-side).</em>

Likewise, we can also conclude that the triangle EFH is congruent to triangle GFH.

5 0

1 year ago