Mathematics, 17.01.2020 00:31 saabrrinnaaa

Clara writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram:

clara's proof

for triangles aob and cod, angle 1 is equal to angle 2, as they are vertical angles.
ao = oc and bo = od because it is given that diagonals bisect each other.
the triangles aob and cod are congruent by sas postulate.
similarly, triangles aod and cob are congruent.
by angle abd is equal to angle cdb and angle adb is equal to angle cbd.
as the alternate interior angles are congruent, the opposite sides of quadrilateral abcd are parallel.
therefore, abcd is a parallelogram.

which is the missing phrase in clara's proof?
cpctc
property of parallelograms
transitive property
vertical angles theorem

Answers: 1

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Answers

Answer from: Quest

ion

step-by-step explanation:

ion ion ion ion ion ion ion ion ion ion ion

Answer from: Quest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

Answer from: Quest

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ

for 3.5 south, y = -3.5

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30

for 15 west, x = -15

total x = 8.2 * cos 30 – 15 ≈ -7.9

total y = -3.5 + 8.2 * sin 30 = 0.6

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5

the magnitude is approximately 7.9 m

tan θ = y/x = 0.6/-7.9

the angle is approximately 4.3˚ north of west

Answer from: Quest

Ithink so 1.you go to your profile and your questions and you'll be able to delete them

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Clara writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each o...