Which of the following shapes has an apex? Select all that apply.

Mathematics

2 answers:

Norma-Jean [14]3 years ago

7 0

Answer:

B. Cone,

E. Pyramid.

Step-by-step explanation:

We are asked to choose the shapes which have an apex.

We know that apex is the highest point of a shape and it is directly above the base of a figure.

Let us check our given choices one by one.

A. Sphere:

We know that sphere is rounded from each side, so it can not have an apex.

B. Cone:

We know that a cone has an apex directly above its base, therefore, option B is the correct choice.

C. Cylinder:

We know that cylinder is a circular shape and it has no apex, therefore, cylinder is not a correct choice.

D. Cube:

We know that cube is a three dimensional figure, whose each side is equal, therefore, cube is not a correct choice either.

E. Pyramid:

Since pyramid's vertices meet directly above its base, therefore, pyramid is the correct choice.

4vir4ik [10]3 years ago

6 0

The answer is a cone and a pyramid!

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In the figure, and bisect each other. Complete the statements to prove that quadrilateral ABCD is a parallelogram.

Alisiya [41]

Observe the figure below.

Statement Reason

1. AC and BD bisect each other Given

2. AE = EC and BE = ED Definition of bisection

3. $m \angle AEB = m \angle CED$ Vertical angle theorem

Vertical angle theorem states " When two lines intersect each other, the vertically opposite angles are always equal".

4. $\Delta ABE \cong \Delta CDE$ SAS criterion for congruence

5. $m \angle ACD = m \angle CAB$ Corresponding angles of congruent triangles are congruent

6. $AB \parallel CD$ Converse of alternate interior angle theorem

7. $m \angle BEC = m \angle AED$ Vertical angle theorem

8. $\Delta BEC \cong \Delta DEA$ SAS criterion for congruence

9. $BC \parallel AD$ Converse of alternate interior angle theorem

As, $\Delta BEC \cong \Delta DEA$ , so $m \angle CBD = m \angle BDA$ as corresponding parts of corresponding triangles are equal. As these angles are alternate interior angles, so the lines BC and AD are parallel by "Converse of alternate interior angle theorem".