Can someone please double check my true and false answers!

1. All cylinders are prisms: TRUE

2. The angle opposite a side length of 6 cm in a triangle is larger than an angle opposite a side length of 7 cm in the same triangle: FALSE

3. The perpendicular bisector of the base of any isosceles triangle also bisects the vertex angle of the triangle: TRUE

4. Each diagonal of a square bisects an opposite angle: true

5. Alternate interior angles are the angles that are both interior to two lines and on alternate sides of the transversal that intersects them: TRUE

1. FALSE

cylinders are generally round. Prisms have sides. Are all circles polygons? Only in the limiting sense that they are polygons with infinitely many sides :-)

2. FALSE
3. TRUE
4. TRUE
5. TRUE

1. I just thought since prisms and cylinders both have 2 bases they might be considered the same...Unlike pyramids that have only 1 base.

No Curves!

A prism is a polyhedron, which means the cross section will be a polygon (a straight-edged figure) ... so all sides will be flat!

To verify the true and false answers, let's go through each statement and explain how to determine the correctness of each one:

1. All cylinders are prisms: TRUE
To confirm this, we need to understand the definitions of a cylinder and a prism. A cylinder is a three-dimensional shape having two congruent circular bases and a curved surface connecting the bases. A prism, on the other hand, has two identical polygonal bases connected by parallelograms. Since a cylinder has circular bases and no polygonal bases, it is not a prism. Therefore, the statement is FALSE, not TRUE.

2. The angle opposite a side length of 6 cm in a triangle is larger than an angle opposite a side length of 7 cm in the same triangle: FALSE
To verify this statement, we need to consider the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, if we have a triangle with side lengths of 7 cm, 6 cm, and x cm (where x represents the unknown length), the inequality would be 7 + 6 > x. Simplifying this, we get 13 > x. In this inequality, x could be any value less than 13, but it cannot be larger than 13. Hence, the statement is FALSE.

3. The perpendicular bisector of the base of any isosceles triangle also bisects the vertex angle of the triangle: TRUE
To validate this statement, we can visualize an isosceles triangle and its properties. An isosceles triangle has two congruent sides and two congruent angles opposite those sides. The perpendicular bisector of the base of an isosceles triangle will pass through the midpoint of the base, dividing it into two equal segments. As a result, this perpendicular bisector will also intersect the vertex angle at its midpoint, essentially bisecting it. Therefore, the statement is TRUE.

4. Each diagonal of a square bisects an opposite angle: TRUE
To verify this statement, we can examine the properties of a square. In a square, all sides and angles are congruent. When a diagonal is drawn, it divides the square into two congruent right triangles. Each right triangle has one of the angles of the square as one of its acute angles. Since both right triangles are congruent, their angles are also congruent. Hence, the diagonal of a square bisects an opposite angle. Therefore, the statement is TRUE.

5. Alternate interior angles are the angles that are both interior to two lines and on alternate sides of the transversal that intersects them: TRUE
To confirm this statement, we need to understand the concept of alternate interior angles. When two parallel lines are intersected by a transversal, alternate interior angles are the pairs of angles on the inside of the parallel lines and on opposite sides of the transversal. By their nature, these angles are congruent or equal in measure. Therefore, the statement is TRUE.

Please note that it's always beneficial to double-check the answers and explanations to enhance your understanding.