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3 years ago

What 3 relationships are truth in the construction below?? (Only if you know please though! I numbered them for you as well!)

Mathematics

1 answer:

Ahat [919]3 years ago

5 0

Answer:

The 3 truth relationships are:

Line CD is the perpendicular bisector of AB ⇒ (1)

Line AB is perpendicular to the line CD ⇒ (3)

Line segment AE is congruent to line segment BE ⇒ (4)

Step-by-step explanation:

When two circles pass through the centers of each other, then the line joining their intersection points is the axis of symmetry (perpendicular bisector) of the segment joining their centers

In the given figure

∵ Circle A passes through the center of circle B

∵ Circle B passes through the center of circle A

∴ AB is the line center

∵ Circles A and B intersected at points C and D

∴ CD is the line joining their intersection points

→ By using the rule above

∴ CD is the perpendicular bisector of AB

∴ Line CD is the perpendicular bisector of AB ⇒ (1)

∵ CD ⊥ AB

→ That means AB is perpendicular to CD

∴ Line segment AB is perpendicular to line CD ⇒ (3)

∵ CD is the perpendicular bisector of AB

∴ E is the mid-point of AB

→ That means E divides AB into two equal parts AE and BE

∴ AE = BE

∴ Line segment AE is congruent to line segment BE ⇒ (4)

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In the trapezoid ABCD (AB∥CD) point M∈AD, so that AM:MD=3:5. Line L ∥AB and going through point M intersects diagonal AC and leg

siniylev [52]

Answer:

$\dfrac{AP}{PC}=\dfrac{3}{5}$

$\dfrac{BN}{CN}=\dfrac{3}{5}$

Step-by-step explanation:

Consider triangles AMP and ADC. In these triangles,

angle A is the common angle, so $\angle MAP\cong \angle DAC$ by reflexive property;
angles AMP and ADC are congruent as corresponding angles when two parallel lines MP and CD are cut by transversal AD.

Hence, triangles AMP and ADC are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

$\dfrac{AM}{AD}=\dfrac{AP}{AC}\\ \\\dfrac{3x}{3x+5x}=\dfrac{AP}{AC}\\ \\\dfrac{AP}{AC}=\dfrac{3}{8}\Rightarrow AP=\dfrac{3}{8}AC\\ \\PC=AC-AP=AC-\dfrac{3}{8}AC=\dfrac{5}{8}AC,$

$\dfrac{AP}{PC}=\dfrac{\frac{3}{8}AC}{\frac{5}{8}AC}=\dfrac{3}{5}$

Consider triangles ACB and PCN. In these triangles,

angle C is the common angle, so $\angle ACB\cong \angle PCN$ by reflexive property;
angles ABC and PCN are congruent as corresponding angles when two parallel lines PN and AB are cut by transversal BC.

Hence, triangles ACB and PCN are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

$\dfrac{CP}{AP}=\dfrac{CN}{CB}\\ \\\dfrac{5x}{3x+5x}=\dfrac{CN}{CB}\\ \\\dfrac{CN}{CB}=\dfrac{5}{8}\Rightarrow CN=\dfrac{5}{8}CB\\ \\BN=BC-CN=BC-\dfrac{5}{8}BC=\dfrac{3}{8}BC,$

$\dfrac{BN}{CN}=\dfrac{\frac{3}{8}BC}{\frac{5}{8}BC}=\dfrac{3}{5}$

4 0

3 years ago

Harvey plans to use 5 ft of shelving for four shelves whose lengths are to be a series of consecutive even numbers. How many inc

IgorC [24]

5 ft = 5 * 12 in = 60 inches
Four consecutive even numbers are: x, x + 2, x + 4, x + 6
x + x + 2 + x + 4 + x + 6 = 60
4 x + 12 = 60
4 x = 60 - 12
4 x = 48
x = 48 : 4
x = 12
Answer:
Those shelves should be: 12, 14, 16 and 18 inches long.
Verification: 12 + 14 + 16 + 18 = 60 in = 5 ft.

7 0

4 years ago

Here is a flower made up of yellow hexagons, red trapezoids, and green triangles. How many copies of this flower pattern could y

RUDIKE [14]

Answer:

Step-by-step explanation:Answer:

Part a) You could build 5 copies of the flower pattern

Part b) You would have 40 red trapezoids left over

Step-by-step explanation:

The complete question in the attached figure

Part a)

Let

x -----> the number of yellow hexagons

y ----> the number of red trapezoids

z ----> the number of green triangles

we know that

The flower pattern has the following ratios

Find out how many copies of this flower pattern could you build if you had 30 yellow hexagons,50 red trapezoids, and 60 green triangles

1) For x=30

Divide 30 by 6 (remember that in one pattern there are 6 yellow hexagons)

Verify the quantity of y needed and the quantity of z needed

Find the value of y

10 < 50 ----> is ok

Find the value of z

45<60 --->is ok

2) For y=50

Divide 50 by 2 (remember that in one pattern there are 2 red trapezoids)

Verify the quantity of x needed and the quantity of z needed

Find the value of x

150 > 30 ----> is not ok

3) For z=60

Divide 60 by 9 (remember that in one pattern there are 9 green triangles)

60/9=6.7 copies

Round down

6 copies -----> 6(9)=54 green triangles

Verify the quantity of x needed and the quantity of y needed

Find the value of x

36> 30 --->is not ok

therefore

You could build 5 copies of the flower pattern

Part b)

we know that

x:y:z=6:2:9

If you build 5 copies

1) You would use 5*6=30 yellow hexagons and you would have 0 hexagons left over

2) You would use 5*2=10 red trapezoids and you would have (50-10=40) trapezoids left over

3) You would use 5*9=45 green triangles and you would have (60-45=15) triangles left over

therefore

You would have 40 red trapezoids left over

8 0

1 year ago

Find the slope of the equation y = 3x + 4

Luda [366]

Answer:

the slope is 3 you are right

Step-by-step explanation:

y=mx+b

where m is the slope.

7 0

4 years ago

Quadrilateral has angles 45 degrees, 150 degrees, 65 degrees, and N degrees

Aleonysh [2.5K]

N=100
other angles=260
all interior angles of a quadrilateral add up to 360

3 0

3 years ago