Fill in the blanks. If the triangles cannot be shown to be congruent from the information given, leave the triangle's name blank
and write CanNot Be Determined (CNBD) in the spot for the rule.
∆ SAT ≅ ∆ ________
By rule _________
QUICKLY PLEASE. I NEED TO DO THIS QUICKLY
∆ SAT ≅ ∆ ________
By rule _________
QUICKLY PLEASE. I NEED TO DO THIS QUICKLY
1 answer:
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Answer:
Exercise 1: The length of the unknown leg is 4 inches.
Exercise 3: The following straws can be used to construct the triangle: b) , c)
, d)
, e)
, f)
Exercise 4: Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)
Step-by-step explanation:
Exercise 1:
Let suppose that triangle represented in the figure is a right triangle, the length of the missing leg is determined by Pythagorean Theorem:
(1)
Where:
- Hypotenuse, in inches.
- Known leg, in inches.
- Unknown leg, in inches.
If we know that and
, then the length of the unknown leg is:
Since 4 is the least whole number closest to , then we conclude that the length of the unknown leg is 4 inches.
Exercise 3:
The range of possible lengths for the missing side of the triangle is represented by the following simultaneous inequality:
(2)
Where:
- Greater side, in inches.
- Lesser side, in inches.
- Missing side, in inches.
If we know that and
, then we have the following range of missing sides:
The following straws can be used to construct the triangle: b) , c)
, d)
, e)
, f)
Exercise 4:
Let check each pair to determine possible constructions by means of the inequality used in Exercise 3:
(i)
Possible choices: 5 inches.
(ii)
Possible choices: 4 inches, 6 inches.
(iii)
Possible choices: 5 inches, 6 inches.
(iv)
Possible choices: None.
(v)
Possible choices: 2 inches, 6 inches.
(vi)
Possible choices: 5 inches.
(vii)
Possible choices: None.
(viii)
Possible choices: 2 inches, 4 inches, 10 inches.
(ix)
Possible choices: 6 inches.
(x)
Possible choices: 5 inches.
Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)