1) True/False. If four sides and one angle of a quadrilateral are congruent to four corresponding sides and a corresponding angle of another quadrilateral, then the quadrilaterals are congruent.
2) Given parallelogram \(NICE\) with \(m\angle{I}=52^{\circ}\), \(NE = 10.3\), and an altitude from \(C\) of \(4.1\). Find the perimeter of \(NICE\).
2) Given parallelogram \(NICE\) with \(m\angle{I}=52^{\circ}\), \(NE = 10.3\), and an altitude from \(C\) of \(4.1\). Find the perimeter of \(NICE\).
5) Given rhombus \(SOUP\) with \(m\angle{S}=120^{\circ}\) and the shortest diagonal has a length of \(6\sqrt{3}\). Find the perimeter of \(SOUP\).
8) Answer with “Always”, “Sometimes”, or “Never” true.
a) All squares are parallelograms, rectangles and rhombuses
b) A parallelogram has congruent diagonals
c) All parallelograms are rectangles
d) All rhombuses are squares
e) A rhombus is a rectangle
f) A rectangle has perpendicular diagonals
g) All rectangles are parallelograms
h) A square can have an interior angle greater than \(90^{\circ}\)
i) Parallelograms, rectangles, rhombuses and squares all have bisecting diagonals
j) Parallelograms, rectangles, rhombuses and squares have two pairs of sides with equal slopes.
k) Parallelograms are rectangles
l) All rhombuses are parallelograms
m) A rectangle has adjacent sides whose slopes are opposite reciprocals of each other
a) All squares are parallelograms, rectangles and rhombuses
b) A parallelogram has congruent diagonals
c) All parallelograms are rectangles
d) All rhombuses are squares
e) A rhombus is a rectangle
f) A rectangle has perpendicular diagonals
g) All rectangles are parallelograms
h) A square can have an interior angle greater than \(90^{\circ}\)
i) Parallelograms, rectangles, rhombuses and squares all have bisecting diagonals
j) Parallelograms, rectangles, rhombuses and squares have two pairs of sides with equal slopes.
k) Parallelograms are rectangles
l) All rhombuses are parallelograms
m) A rectangle has adjacent sides whose slopes are opposite reciprocals of each other
9) \(ABCD\) is a parallelogram. Point \(P\) on \(\overline{AB}\) divides it in the ratio \(AP:PB = 3:2\), and point \(Q\) on \(\overline{CD}\) divides it in the ratio \(CQ:QD = 7:3\). Let \(R\) be the intersection of \(\overline{PQ}\) and \(\overline{AC}\). Then, \(AR:AC = a:b\), where \(a\) and \(b\) are positive coprime integers. What is \(a + b\)?
From brilliant.org |
10) Given: Parallelogram \(RELO\) with \(m\angle R = (4x + 3y)^{\circ}\), \(m\angle E = (3x - 15)^{\circ}\), and \(m\angle L =(5y)^{\circ}\).
Find: \(m\angle O\)
11) Given: Parallelogram \(GRAM\) with \(m\angle G = (x + 3y)^{\circ}\), \(m\angle R = (x - 4)^{\circ}\), and \(m\angle A = (4y - 8)^{\circ}\).
Find: \(m\angle M\)
12) One diagonal of a parallelogram divides the parallelogram into two congruent triangles. Prove this.
Solution Bank
Find: \(m\angle O\)
11) Given: Parallelogram \(GRAM\) with \(m\angle G = (x + 3y)^{\circ}\), \(m\angle R = (x - 4)^{\circ}\), and \(m\angle A = (4y - 8)^{\circ}\).
Find: \(m\angle M\)
12) One diagonal of a parallelogram divides the parallelogram into two congruent triangles. Prove this.
Solution Bank