State whether or not the following triangles are similar. If not, explain why not. If so, write a similarity statement

Mathematics

1 answer:

valentinak56 [21]3 years ago

7 0

9514 1404 393

Answer:

a) ∆RLG ~ ∆NCP; SF: 3/2 (smaller to larger)

b) no; different angles

Step-by-step explanation:

a) The triangles will be similar if their angles are congruent. The scale factor will be the ratio of any side to its corresponding side.

The third angle in ∆RLG is 180° -79° -67° = 34°. So, the two angles 34° and 67° in ∆RLG match the corresponding angles in ∆NCP. The triangles are similar by the AA postulate.

Working clockwise around each figure, the sequence of angles from lower left is 34°, 79°, 67°. So, we can write the similarity statement by naming the vertices in the same order: ∆RLG ~ ∆NCP.

The scale factor relating the second triangle to the first is ...

NC/RL = 45/30 = 3/2

b) In order for the angles of one triangle to be congruent to the angles of the other triangle, at least one member of a list of two of the angles must match for the two triangles. Neither of the numbers 57°, 85° match either of the numbers 38°, 54°, so we know the two triangles have different angle measures. They cannot be similar.

You might be interested in

You need to purchase supplies for the trip. You have $1000 to spend.

SCORPION-xisa [38]

Answer:

241.50

Step-by-step explanation:

Oxen= 40 x 2 = 80

Food=0.20 x 500 =100

Clothing = 10 x 5 = 50

total = 230

Tax= 5 percent x 230 divided by 100

= $11.50

230 +11.50

= 241.50

6 0

2 years ago

(6-7)[4-6]^2+2(-4)-2]

horsena [70]

This answer would be (-14).

6 0

2 years ago

-2 (3 + 5y -10) = 34

IrinaK [193]

-2 (3+5y-10) = 34
Step 1) -6-10y+20=34
Step 2) -10y+20=40
Step 3) -10y=20
Step 4) y = -2
Answer is -2

7 0

3 years ago

Read 2 more answers

Determine what type of model best fits the given situation:

lyudmila [28]

Let value intially be = P

Then it is decreased by 20 %.

So 20% of P = $\frac{20}{100} \times P = 0.2P$

So after 1 year value is decreased by 0.2P

so value after 1 year will be = P - 0.2P (as its decreased so we will subtract 0.2P from original value P) = 0.8P-------------------------------------(1)

Similarly for 2nd year, this value 0.8P will again be decreased by 20 %

so 20% of 0.8P = $\frac{20}{100} \times 0.8P = (0.2)(0.8P)$