in the pair of triangle, write the similarity statement and identify the postulate of theorem that justifies the similarity.

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

6 0

Answer:

ΔEFG ~ ΔRPQ - Angle Angle Angle Theorem

ΔEFG ~ ΔRFQ - Side Side Side Proportional Theorem

Step-by-step explanation:

First set : using triangle sum theory to find missing angle. Letters should match congruent angles when creating statement.

Second set :

$\frac{EG}{RQ}$ = $\frac{10}{12}$ = $\frac{5}{6}$

$\frac{EF}{RF}$ = $\frac{15}{18}$ = $\frac{5}{6}$

$\frac{FG}{FQ}$ = $\frac{20}{24}$ = $\frac{5}{6}$

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Katie is buying souvenir.gifts for her big family back home. She wants to buy everyone either a key chain or a magnet. The magne

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The total number of gifts = x+y.
The inequality is:
$x+y \geq 24$

Key chains cost $1, Magnets $0.50
Total Cost = x + 0.5y
Inequality is:
$x+0.5y \leq 20$

Without graphing you can solve system by using substitution:
$y = 24 - x \\ \\ x + 0.5(24-x) = 20 \\ \\ 0.5x +12 = 20 \\ \\ x = 16 \\ \\ y = 24-16 = 8$

This is one solution where the maximum x value is given.
So the most keychains that can be purchased is 16. However, because magnets are cheaper, more can be purchased as long as cost remains under 20.

If you solve both inequalities for "y", you get the upper and lower bounds for how many magnets can be purchased given a quantity of keychains.

$24-x \leq y \leq 40 -2x \\ \\ x \leq 16$

This is complete solution which gives all possible combinations.
(Graph is Attached)