Question

Quadrilateral HOME is similar to quadrilateral TRAP. Complete the statements below with the missing angle measures. Show work or explain your answer.

𝑚∠M = ___

HOME TRAP
O= 124 A= 47
T= 79
E=110

Answer 1

Since the quadrilaterals HOME and TRAP are similar, the corresponding angles are proportional.

The missing angle measure, m∠M, corresponds to angle A in quadrilateral TRAP.

So, m∠M = 47.

Answer 2

Quadrilateral HOME is similar to quadrilateral TRAP. Complete the statements below with the missing angle measures. Show work or explain your answer.
𝑚∠R = ___

HOME TRAP
O= 124 A= 47
T= 79
E=110

Answer 3

In similar quadrilaterals, corresponding angles are equal.

Since angle R in quadrilateral HOME corresponds to angle T in quadrilateral TRAP, we have:

m∠R = m∠T = 79.

Therefore, m∠R = 79.

Answer 4

Quadrilateral WORD is similar to quadrilateral BANK. What is the length of segment KN?
WORD BANK
BK=4cm
WD=10cm
DR=16cm

Answer 5

Since the quadrilaterals WORD and BANK are similar, the ratios of the corresponding sides are equal.

The ratio of corresponding sides WK/WB = OD/BA = RD/KN

From the given information:
WD = 10 cm and DR = 16 cm => WR = 26 cm (WD + DR)

Now, we can set up the proportion:
(10 + KN)/4 = 26/KN

Solving for KN:

10 + KN = (26*4)/KN
KN^2 + 10KN = 104
KN^2 + 10KN - 104 = 0
Solving this quadratic equation, we get:
KN = 8 cm (K = 8cm - N = 4cm) or KN = -13 (not valid in this context)

Therefore, the length of segment KN is 8 cm.

Answer 6

Given:`∆`COT ~`∆`CAN; Segment CN is equal to 21 inches.
a) Set up a proportion to represent the relationship between the corresponding sides of these triangles to find the length of segment OT.

Answer 7

Since the triangles ∆COT and ∆CAN are similar, the ratio of corresponding sides will be equal.

Let x be the length of segment OT.

The proportion can be set up as follows:

OT/CN = CT/CA

Substitute the given values:
x/21 = CT/CA

Now, we need to find the ratio of the sides CT and CA. Since the triangles are similar, the ratio of corresponding sides will hold:

CT/CA = OT/CN

Substitute the known values:
CT/21 = x/21

Solving for CT:
CT = x

Therefore, the proportion representing the relationship between the corresponding sides is x/21 = x/21.

Answer 8

b) What is the length of segment OT?

Answer 9

From the established proportion:

x/21 = x/21

Cross multiplying:

21x = 21x

Since this equation is true for all values of x, it means that x could be any value, or in other words, it is not possible to determine the length of segment OT with only the given information.

Answer 10

The diagram below shows quadrilateral FORK. Find the missing angle measure
FORK
F= x
O= 64
R=97
K=91

Answer 11

To find the missing angle measure, we need to remember that the sum of the interior angles of a quadrilateral is always 360 degrees.

Given that F = x, O = 64, R = 97, and K = 91, we can set up an equation to find the missing angle:

F + O + R + K = 360

Substitute the known angle measures:
x + 64 + 97 + 91 = 360

Combine the angles:
x + 252 = 360

Subtract 252 from both sides:
x = 360 - 252
x = 108

Therefore, the missing angle measure F is 108 degrees.