Answer:
The true statements include
- The lengths of corresponding edges are in a 1:1 ratio.
- The volumes are equal.
- The base areas are equal.
- The prisms have the same height.
The false statements include;
- Corresponding angles have different measures.
- Corresponding faces are not congruent.
Step-by-step explanation:
In geometry, congruence of two figures or structures indicate that the two figures are of the same size and shape
- Angles are congruent when they are the same size (in degrees or radians).
- Sides are congruent when they are the same length.
So, for congruent prisms, the corresponding angles are expected to be of the same sizes and the corresponding sides are expected to be of the same length.
Taking each of the statements one at a time
- The lengths of corresponding edges are in a 1:1 ratio.
Since we have concluded that the corresponding sides of congruent structures/figures/prisms are of the same length. This statement has to be true.
- The volumes are equal.
Since all the corresponding sides are of the same length and the shapes are similar, the volume has to be equal. This statement is true.
- Corresponding angles have different measures.
We have postulated above that corresponding angles of congruent structures/figures/prisms are of the same sizes or measures. So, this statement is false.
- Corresponding faces are not congruent.
Since we have concluded that the corresponding sides of congruent structures/figures/prisms are of the same length. Corresponding faces have to be congruent then. So, this statement is false.
- The base areas are equal.
Since all the corresponding sides are of the same length and the shapes are similar, the base areas are equal. This statement is true.
- The prisms have the same height.
Since all the corresponding sides are of the same length and the shapes are similar, the prisms have to have the same height because the heights are corresponding sides. This statement is true.
Hope this Helps!!!
