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Nezavi [6.7K]
3 years ago
12

Diagonals AC and BD form right angles at point M in parallelogram ABCD. Prove ABCD is a rhombus.

Mathematics
2 answers:
Tanya [424]3 years ago
5 0
1. Consider the parallelogram ABCD drawn in the 1. figure attached.

2. The diagonals of a parallelogram bisect each other, so AM=MC and BM=MD


3. In triangle ABC, BM is an altitude (BM perpendicular to AC), but also a median (AM=MC). An altitude is also a median only when the triangle is isosceles, so AB=BC 

similarly, in triangle BCD, CM is both an altitude and a median.Thus, BCD is an isosceles triangle so BC=CD.

4. AB= DC (opposite sides of a parallelogram are equal), similarly BC=DA

5. So ABCD is a quadrilateral, with all 4 sides equal in length. Thus ABCD is a rhombus. 

BabaBlast [244]3 years ago
5 0

The correct answer is:

B. △AMB ≅ △CMB ≅ △CMD ≅ △AMD

|Huntrw6|

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Spencer made a quilt for his cousin's doll. The quilt had a 7x7 array of different color square patches. If each patch is 1 3/4
Damm [24]

Answer:

\frac{2401}{16} square inches

Step-by-step explanation:

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The quilt made by Spencer had a 7×7 array of different color square patches such that each patch is 1\frac{3}{4} in long.

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Side of each quilt = 7(\frac{3}{4})=7(\frac{7}{4})=\frac{49}{4}

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3 0
3 years ago
Solve: -3= 12x-5(2x-7)
leonid [27]

Answer:

x = -19

Step-by-step explanation:

-3= 12x-5(2x-7)

Distribute

-3= 12x-10x+35

Combine like terms

-3 = 2x +35

Subtract 35 from each side

-3-35 = 2x+35-35

-38 = 2x

Divide each side by 2

-38/2 = 2x/2

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7 0
3 years ago
A glass is 4/7 full . Then 70cm3 of orange juice is poured in . The glass is now 2/4 full. What is the total volume of the glss
Korolek [52]
Let 
x--------------> total volume of a glass

we know that
(4/7)x-70=(2/4)x------------> (4/7)x-70=(1/2)x--------> 2*(4/7)x-2*70=x
(8/7)x-140=x

<span>multiplied by 7 the expresion
</span>7*(8/7)x-7*140=7*x-----------> 8x-980=7x--------> x=980 cm³

the answer is 
<span>the total volume of the glass is 980 cm</span>³
3 0
3 years ago
Read 2 more answers
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