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2 years ago

Look at the picture

Mathematics

1 answer:

valentina_108 [34]2 years ago

6 0

9514 1404 393

Answer:

Step-by-step explanation:

When angles are between the parallel lines, they are called interior. If they are both on the same side of the transversal, they are "same-side interior."

If angles are on opposite sides of the transversal, they are exterior.

If angles are in the same direction from the intersection point, they are corresponding.

Angles in opposite directions from the point of intersection are vertical angles.

same-side interior: {3, 5} and {4, 6}. (supplementary)

same-side exterior: {1, 7} and {2, 8}. (supplementary)

alternate interior: {3, 6} and {4, 5}. (congruent)

alternate exterior: {1, 8} and {2, 7}. (congruent)

corresponding: {1, 5}, {2, 6}, {3, 7}, {4, 8}. (congruent)

vertical: {1, 4}, {2, 3}, {5, 8}, {6, 7}. (congruent)

Angles 6 and 4 are same-side interior angles; their sum is 180°.

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Step-by-step explanation:

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2 years ago

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

melamori03 [73]

Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by: