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ioda
3 years ago
15

Since ABCD is a parallelogram, the two pairs of _________ sides (AB¯ and CD¯, as well as AD¯ and BC¯) are congruent. Then, since

∠9 and ∠11 are vertical angles, it can be concluded that ∠9≅∠11. Since ABCD is a parallelogram, AB¯∥CD¯. Since ∠2 and ∠5 are alternate interior angles along these parallel lines, the Alternate Interior Angles Theorem allows that ∠2≅∠5. Since two angles of △AEB are congruent to two angles of △CED, the Third Angles Theorem supports that ∠8≅∠3. Therefore, using the _________, it can be stated that △AEB≅△CED. Then, applying the definition of congruent triangles, it can be stated that AE¯≅CE¯, which makes E the midpoint of AC¯. Use a similar argument to prove that △AED≅△CEB; then it can be concluded that E is also the midpoint of BD¯. Since the midpoint of both line segments is the same point, the segments bisect each other by definition. Match each number (1 and 2) with the word or phrase that correctly fills in the corresponding blank in the proof.
Mathematics
1 answer:
Marysya12 [62]3 years ago
7 0

Answer:

1. Opposite

2. angle-side-angle criterion

Step-by-step explanation:

Since ABCD is a parallelogram, the two pairs of <u>(opposite)</u> sides (AB¯ and CD¯, as well as AD¯ and BC¯) are congruent. Then, since ∠9 and ∠11 are vertical angles, it can be concluded that ∠9≅∠11. Since ABCD is a parallelogram, AB¯∥CD¯. Since ∠2 and ∠5 are alternate interior angles along these parallel lines, the Alternate Interior Angles Theorem allows that ∠2≅∠5. Since two angles of △AEB are congruent to two angles of △CED, the Third Angles Theorem supports that ∠8≅∠3. Therefore, using the <u>(angle-side-angle criterion)</u>, it can be stated that △AEB≅△CED. Then, applying the definition of congruent triangles, it can be stated that AE¯≅CE¯, which makes E the midpoint of AC¯. Use a similar argument to prove that △AED≅△CEB; then it can be concluded that E is also the midpoint of BD¯. Since the midpoint of both line segments is the same point, the segments bisect each other by definition. Match each number (1 and 2) with the word or phrase that correctly fills in the corresponding blank in the proof.

A parallelogram posses the following features:

   1. The opposite sides are parallel.

   2. The opposite sides are congruent.

   3. It has supplementary consecutive angles.

   4. The diagonals bisect each other.

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Is this set of ratios equal?: 4/7 and 9/13
wel

Answer:

NO this set is not equivalent

Step-by-step explanation:

Okay the way you find out if a pair of ratios are equal is you would divide the denominator and nominator with each other, so: 13/7 and 9/4. But sense the answer would be in decimal form and cant be simplified this wouldnt be considered equivalent.  Also if you divide 7 by 4 you get a different answer than when you do 13 divided 9.

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CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION?
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  B.  More than one quadrilateral exists with the given conditions, and all instances must be isosceles trapezoids.

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary. They are only congruent if the parallelogram is a rectangle. In this problem, adjacent angles are both congruent and acute. If this were a triangle, it would guarantee the triangle is isosceles.

The fact that opposite angles are supplementary guarantees that the fourth side of the figure is parallel to the base between the acute angles. That makes the figure an isosceles trapezoid. Unless specific angles and side lengths are specified, the description matches <em>any</em> isosceles trapezoid.

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3 years ago
Simplify the following 3√28-5√63+4√112
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7√7

using the ' rule of radicals '

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√63 = √(9 × 7) =√9 × √7 = 3√7

√112 = √(16 × 7 ) = √16 × √7 = 4√7

substituting into the expression

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2 years ago
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3 years ago
Write an inequality to match each description. Use n for the variable.
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{\huge {\mathfrak {Answer :-}}}

Let, the length be l and breadth be b.

So, 2(l + b) = 26

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Or, l = 13 - b

So, we may write like this,

Area = l * b

Or, l * b > 30

Or, l (13 - l) > 30

Or, 13l - l^2 > 30

Or, l^2 - 13l + 30 > 0

Or, l^2 - 3l - 10l + 30 > 0

Or, l(l - 3) - 10(l - 3) > 0

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Length > 7

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That's it..

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