Quadrilaterals Exercises

How can you be certain that a square is a rhombus?

Hint

You don't need to write a formal proof. We won't stop you if that's what you want to do, but we're just saying it isn't necessary.

The quadrilateral ABCD is a square. If the length of AB is 2a, how long are AC and BG in terms of a?

Hint

Remember all that talk about 45-45-90 triangles? Well, it's important.

The quadrilateral ABCD is a square. What is the measure of ∠AGD?

Hint

What can we say about the diagonals of a square?

The quadrilateral ABCD is a square. Show that ∠GCB measures 45°.

Hint

A square is a square, sure. But what other types of quadrilaterals can it be?

If ABCF and FCDE are both squares, show that ΔACE ~ ΔCDE.

Hint

With this question, as with photography, it's all about angles.

JOHN is a square and HA ≅ NA. Prove that ΔJAO is isosceles.

Hint

Congruent triangles are there for you, always and forever. Even in squares.

Statements	Reasons
1. JOHN is a square	Given
2. HA ≅ NA	Given
3. OH ≅ JN	All sides of a square are congruent (1)
4. m∠N = m∠H = 90°	All interior angles of a square are 90° (1)
5. ∠N ≅ ∠H	Definition of congruent angles (4)
6. ΔANJ ≅ ΔAHO	SAS Postulate (2, 3, 5)
7. JA ≅ OA	CPCTC (6)
8. ΔJAO is isosceles	Definition of isosceles triangle (7)