In this question we should fill the blanks based all information related to Euclidean geometry, especially concepts related to angles, triangles, parallelism and quadrilaterals.

The complete paragraph is shown below:

Since AD is parallel to BC, alternate interior angles.

AD and BC are congruent.

AC is congruent to AC since segments are congruent to themselves.

Along with the given information that AD is congruent to BC, triangle ADC is congruent to triangle CBA by the Side-Angle-Side Triangle Congruence.

Since the triangles are congruent, all pairs of corresponding angles are congruent, so angle DCA is congruent to angle BAC.

Since those alternate interior angles are congruent. AB must be parallel to CD.

Since we define a parallelogram as a quadrilateral with both pairs of opposite sides parallel, ABCD is a parallelogram.

To learn more on quadrilaterals, we kindly invite to check this verified question: brainly.com/question/25240753

8 0

2 years ago

Help Plss simply can u show step by step ?-4(8x-4)+3x

Vikentia [17]

Answer:

-4(8x-4)+3x = -29x+16

Step-by-step explanation:

1. Simplify -4(8x-4) by using the distribution property:

-4(8x) = -32x and -4(-4) = 16 so -4(8x-4) = -32x+16

2. Add 3x to the remaining equation:

-32x+16+3x = -29x+16

3. The answer is:

-29x+16

6 0

2 years ago

What is an equation of the line that passes through the points (-2, -5) and (-1, 1)?

Dennis_Churaev [7]

Answer: y=6x+7

Step-by-step explanation:

To find the equation of the line, we want to find the slope with the formula $m=\frac{y_2-y_1}{x_2-x_1}$ .

$m=\frac{1-(-5)}{-1-(-2)} =\frac{6}{1}=6$

Now that we know th eslope, we can start to fill out the equation. To find the y-intercept, we can plug in a given point and solve.

y=6x+b

1=6(-1)+b [multiply]

1=-6+b [add both sides by 6]

b=7

Now, we know the equation is y=6x+7.

8 0

2 years ago

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