Help PLZ Kinda been confused

Mathematics

1 answer:

natka813 [3]3 years ago

7 0

9514 1404 393

Answer:

use the transitive property and the congruence of vertical angles

Step-by-step explanation:

First of all, look at the figure and the given information, and see how that relates to the question being asked.

Here, you're given several angles between the lines of interest, all of which are congruent, and you're asked to show the lines are parallel. Two of the given angles (1 and 4) are "alternate interior angles", so the theorem relating those to parallel lines is useful.

Statement . . . . Reason

1. ∠1 ≅ ∠2, ∠3 ≅ ∠4 . . . . 1. Given

2. ∠2 ≅ ∠3 . . . . 2. Vertical angles are congruent

3. ∠1 ≅ ∠3 . . . . 3. transitive property of congruence*

4. ∠1 ≅ ∠4 . . . . 4. transitive property of congruence

5. k ║ l . . . . 5. Converse of alternate interior angles theorem**

_____

* The transitive property tells you if a ≅ b and b ≅ c, then a ≅ c.

** The alternate interior angles theorem says the alternate interior angles at a transversal crossing parallel lines are congruent. The converse says if those angles are congruent, then the lines are parallel.

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Rus_ich [418]

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Explain how to use what you know about the sum of the angles in a triangle to figure out the sum of the angles of quadrilateral

Elena L [17]

Answer:

See attached image and explanation below.

Step-by-step explanation:

We notice that any quadrilateral abed can be divided into two triangles by drawing one of the quadrilateral's diagonals. See the attached picture where the quadrilateral is noted with a green perimeter, the diagonal is pictured in red, and the triangles that are form are shaded in light blue and beige.

Each of the triangles in which the quadrilateral is divided, has the property that the addition of its internal angles equals 180 degrees. From the picture we understand that in order to find what the addition of the internal angles of the quadrilateral is, all we need to do is to add all the angles in both triangles.

Such addition will render 360 degrees. And since the diagonal division can be done with a quadrilateral of any shape, we conclude that the addition of the internal angles of any quadrilateral should result in 360 degrees.