Quadrilaterals and Parallelograms
It is a quadrilateral with 4 congruent angles and 4 congruent sides.
Square
DM = 5 cm
Represent 1/3 = 3/9 using inverse property.
3/1 = 9/3 or 3 = 3
_______________ states that two polygons are similar if and only if the corresponding angles are congruent and corresponding sides are proportional.
Similar Polygons Theorem
Given a right triangle where a = 3 and b = 4, find the value of c.
Suppose that LOVE is a parallelogram. If LO = 3x - 7 and EV = x + 9, find the value of x.
x = 8
Given that CALM is an isosceles trapezoid where ∠C = 50°. Find ∠A.
∠A = 50°
The ratio of the boys to girls in 9 - Helium is 3:5. If 9 - Helium consists of 40 students, find how many boys are there in 9 - Helium.
15
ABC and DEF are similar right triangles, with DEF being smaller than ABC. If AB = 2, BC = 6, AC = x, while DE = 1, EF = 3, and DF = 5, find AC if DE/AB = EF/BC = DF/AC.
AC = 10
In a 45°-45°-90° right triangle, a leg measures 2 cm. What is the measure of the hypotenuse?
2√2 cm
Given that ROSE is a parallelogram, where diagonals intersect at L. Find the value of RL if the measurement of RS is 16 meters.
8 meters
Given triangle ABC with DE as its midsegment. If DE = 14 hm, find the measure of BC.
BC = 28 hm
If m:3 and n:2, what is n:m?
2:3
This similarity theorem states that if two triangles of one triangle are congruent to two angles of a second triangle, then two angles are similar.
AA Similarity Theorem
In a 30°-60°-90° right triangle, the hypotenuse is 6 mm. What is the measure of the shorter leg?
3 mm
If quadrilateral LISA is a rhombus where ∠ LAS = 30°, find the measure of ∠L.
120°
Given that JOAN is a kite. Find the measure of diagonal JA if the area of JOAN is 40 m2 and NO = 8 m.
JA = 10 m
Kare-kare serves 8 people for 1 kilo of beef towel. If Jane wants to cook kare-kare for 40 people, how many kilos of beef towel does she needs?
5 kilos
ABC and DEF are similar right triangles, with ABC being smaller than DEF. If AB = 4, BC = x, AC = y, while DE = 12, EF = 18, and DF = 24 , find x and y if AB/DE = BC/EF = AC/DF.
x = 6 and y = 8
Justine's shuttlecock flies over to the roof. She placed a ladder that is 20 meters long in an angle of 30 degrees on the side of her house so that she can reach the roof and get her shuttlecock. Find out how far she should place the foot of the ladder from the base of her house so that she can easily reach the shuttlecock from the roof.
10 meters
Given that SEAL is a rectangle where the diagonals bisect at T. If ST + TA = 30 cm, find the measure of LT.
LT = 15 cm
Given that quadrilateral MINA is a kite. MA is twice MI. If the perimeter of MINA is 60 cm, find the measure of MI.
MI = 20 cm
The total number of students who joined the Math Club in Manggahan High School is 300. The ratio of the students in Grade 7, 8, 9, and 10 who joined the club is 1:2:3:4, respectively. How many Grade 9 students joined the Math Club?
90 students
This theorem states that the angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle. What similarity theorem is described?
Triangle Angle Bisector Theorem
On a rainy day, Michaella and Miguel decided that they must break up and move on from each other after being in a relationship for 2 years. They decided to part ways at the same time from where they first met. Miguel walked 8 meters north away, while Michaella runs 15 meters east crying. How far are they from each other at that time?
17 meters