Question:
A. 1) Only some squares are rectangles. 2) Rectangles have 4 right angles. 3) Therefore, only some squares have 4 right angles.
B. 1) Only some squares are rectangles. 2) Rectangles have 4 sides that are the same length. 3) Therefore, only some squares have 4 sides that are the same length.
C. 1) All squares are rectangles. 2) Rectangles have 4 sides that are the same length. 3) Therefore, all squares have 4 sides that are the same length.
D. 1) All squares are rectangles. 2) Rectangles have 4 right angles. 3)Therefore, all squares have 4 right angles.
Answer:
All squares are rectangles. Rectangles have 4 right angles. Therefore, all squares have 4 right angles.
Explanation:
Let's go by process of elimination. Starting with A.
A. 1) Only some squares are rectangles. 2) Rectangles have 4 right angles. 3) Therefore, only some squares have 4 right angles.
You can already tell that it's incorrect just looking at sentence 1). All squares are rectangles because a rectangle is:
1. Quadrilateral.
2. Two pairs of parallel sides.
3. Four right angles.
Sentence 2) is correct because Rectangles have 4 right angles. But sentence 3) is incorrect because all squares have 4 right angles.
Down to B.
B. 1) Only some squares are rectangles. 2) Rectangles have 4 sides that are the same length. 3) Therefore, only some squares have 4 sides that are the same length.
Same thing in the first sentence as A . Sentence 1) is incorrect since all squares are rectangles. Sentence 2) is also incorrect because Rectangles do not have the same lengths on all four sides. Only two sides are the same in length. The sides that are the same are the two sides across from each other. Sentence 3) is also incorrect since all squares have 4 sides that are the same length.
Moving down again to C.
C. 1) All squares are rectangles. 2) Rectangles have 4 sides that are the same length. 3) Therefore, all squares have 4 sides that are the same length.
Sentence 1) is correct. All squares are rectangles. Sentence 2) is incorrect because not all sides are the same length. Sentence 3) is correct because all squares have 4 sides that are the same length.
Down to D. (The correct answer.)
D. 1) All squares are rectangles. 2) Rectangles have 4 right angles. 3)Therefore, all squares have 4 right angles.
Sentence 1) is correct because all squares are in fact, rectangles. here is a fact about squares:
"A square is a quadrilateral with all four angles, right angles, and all four sides of the same length. So a square is a special kind of rectangle, it is one where all the sides have the same length. Thus every square is a rectangle because it is a quadrilateral with all four angles right angles."
Sentence 2) is also correct because all rectangles have four right angles. Here are some more facts about rectangles:
"All rectangles are parallelograms, but all parallelograms are not rectangles.
The diagonals of a rectangle divide the rectangle into four triangles.
Every square is a rectangle, but every rectangle is not a square."
Sentence 3) is correct. All squares have 4 right angles. Therefore, Option D. would be your correct answer.