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bagirrra123 [75]
3 years ago
8

EASY BRAINLIEST PLEASE HELP!!

Mathematics
2 answers:
DedPeter [7]3 years ago
6 0

Answer:

C. AB = 5.8 cm

Step-by-step explanation:

In trapezoid ABCD, EF is the Midsegment.

.:. EF = {(AB+CD)

.:: 9.2 = {(AB + 12.6)

:: 9.2 x 2 = AB + 12.6

.. 18.4 = AB + 12.6

.. 18.4-12.6 = AB

:: AB = 5.8 cm

adell [148]3 years ago
4 0

Answer:

Solution given:

Since it is a isosceles trapezoid so it diagonal will be congruent so

PR=QS

PT+RT=12cm

4.9+RT=12cm

RT=12-4.9

RT=7.1cm

PS=QR

QR=9cm

m<QPR=44° base angle of isosceles triangle

m<PTQ=180°-44-44=92°[interior angle remaining of traingle]

m<STR=m<PTQ

m<STR=92°

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How do you prove each of the following theorems using either a two-column, paragraph, or flow chart proof?
lilavasa [31]

All the theorems are proved as follows.

<h3>What is a Triangle ?</h3>

A triangle is a polygon with three sides , three vertices and three angles.

1. The Triangle sum Theorem

According to the Triangle Sum Theorem, the sum of a triangle's angles equals 180 degrees.

To create a triangle ABC, starting at point A, move 180 degrees away from A to arrive at point B.

We turn 180 degrees from B to C and 180 degrees from C to return to A, giving a total turn of 360 degrees to arrive to A.

180° - ∠A + 180° - ∠B + 180° - ∠C = 360°

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2. Isosceles Triangle Theorem

Considering an isosceles triangle ΔABC

with AB = AC, we have by sine rule;

\rm \dfrac{sinA}{BC} =  \dfrac{sinB}{AC} =  \dfrac{sinC}{AB}\\

as AB = AC

sin B = sin C

angle B = angle C

3.Converse of the Isosceles theorem

Consider an isosceles triangle ΔABC with ∠B= ∠C, we have by sine rule;

\rm \dfrac{sinA}{BC} =  \dfrac{sinB}{AC} =  \dfrac{sinC}{AB}\\

as  ∠B= ∠C ,

AB = AC

4. Midsegment of a triangle theorem

It states that the midsegment of two sides of a triangle is equal to (1/2)of the third side parallel to it.

Given triangle ABC with midsegment at D and F of AB and AC respectively, DF is parallel to BC

In ΔABC and ΔADF

∠A ≅ ∠A

BA = 2 × DA, BC = 2 × FA

Hence;

ΔABC ~ ΔADF (SAS similarity)

BA/DA = BC/FA = DF/AC = 2

Hence AC = 2×DF

5.Concurrency of Medians Theorem

A median of a triangle is a segment whose end points are on vertex of the triangle and the middle point of the side ,the medians of a triangle are concurrent and  the point of intersection is inside the triangle known as Centroid .

Consider a triangle ABC , X,Y and Z are the midpoints of the sides

Since the medians bisect the segment AB into AZ + ZB

BC into BX + XB

AC into AY + YC

Where:

AZ = ZB

BX = XB

AY = YC

AZ/ZB = BX/XB = AY/YC = 1

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the median segments AX, BY, and CZ are concurrent (meet at point within the triangle).

To know more about Triangle

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8 0
1 year ago
gavin deposited $1500 into his savings account that is compounded quarterly at an interest rate of 1.5%. How munch money will ga
creativ13 [48]

<u>Answer:</u>

The money will gavin have after 5 years is 1616.59$

<u>Explanation:</u>

We know that compound interest is given by  

A=P\left(1+\frac{r}{n}\right)^{n t}

          Where A = final amount

       P = Principal amount = $1500 (given)

r  = interest rate = 1.5% = 0.015

n = no. of times interest applied per time period = given quarterly = 4

t = time period = 5 years  

    So,

A=1500\left(1+\frac{0.015}{4}\right)^{4 \times 5}

1500\left(1+\frac{0.015}{4}\right)^{20}

 = 1616.59$ which is the money will gavin have after 5 years

4 0
3 years ago
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