McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
5. Rhombi and Squares
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Exercise 17 Page 518

What quadrilaterals do have all sides congruent?

Rhombus, see solution.

Practice makes perfect
Let's look at the given picture. Since we know that all crosswalks are the same length, we will recall that a quadrilateral with all sides congruent can be either a rhombus or a square.

In our exercise, we are given that the angle between two streets has a measure of 29^(∘). This means that one of the angles of this quadrilateral is also 29^(∘), as it creates a pair of vertical angles with the given one.

Notice that a square has four right angles, as it is both a rectangle and a rhombus. Therefore, this quadrilateral cannot be a square because it has an angle that is not a right angle. This means that this quadrilateral is a rhombus.