1. Advanced Geometry Polygons Lesson 4
Other Quadrilaterals

2. Characteristics of Rectangles
four right angles
Characteristics of Rectangles
Diagonals are congruent.
All characteristics of a parallelogram are still true.

3. Characteristics of Rhombi
Rhombus
Plural: Rhombi
four congruent sides
Characteristics of Rhombi
The diagonals are perpendicular.
Each diagonal bisects a pair of
opposite angles.
All characteristics of parallelograms apply.

4. Squares Characteristics of Squares both a rectangle and a rhombus
All characteristics of a rectangle apply.
All characteristics of a rhombus apply.
All characteristics of a parallelogram apply.

5. Kites
two distinct pairs of adjacent congruent sides

6. Trapezoids Parts of a Trapezoid exactly one pair of parallel sides
bases –
the parallel sides
legs –
the non-parallel sides
base angles –
a pair of angles that touch a base

7. Characteristics of Isosceles Trapezoids
congruent legs
Characteristics of Isosceles Trapezoids
Each pair of base angles is congruent.
The diagonals are congruent.

8. Median of a Trapezoid segment joins the midpoints of the legs36 28
* The median is parallel to the bases.
* The length of the median is half the sum of the bases.

9. Example:
Quadrilateral RSTU is a rectangle. If RT = 6x + 4
and SU = 7x – 4, find x.

10. Example:
Quadrilateral LMNP is a rectangle. If
m∠MNL = 6y + 2, m∠MLN = 5x + 8,
and m∠NLP = 3x + 2, find x.

11. Use rhombus LMNP and the given information to
Example:
Use rhombus LMNP and the given information to
find the value of each variable.
Find m∠PNL if m∠MLP = 64.
Find y if m∠1 = y² - 54.

12. Example:
DEFG is an isosceles trapezoid with median
a) Find DG if EF = 20 and MN = 34.
b) Find m∠1, m∠2, m∠3, & m∠4, if
m∠1 = 3x + 5 and m∠3 = 6x – 5.

13. Given each set of vertices, determine whether
Example:
Given each set of vertices, determine whether
quadrilateral EFGH is a rhombus, a rectangle, or a
square. List all that apply. Explain your reasoning.

14. Show that if LNPR is a rectangle and ,
then
Given:
Prove:
Proof:
Statements:
Reasons: