Are the two triangles below similar? Triangles GHI and JKL are shown. Angle G equals 46 degrees, Angle I equals 27 degrees, Angl
e K equals 108 degrees, Angle L equals 27 degrees, side GH equals 4, side HI equals 5, side KJ equals 2, side JL equals 4.
Yes; they have congruent corresponding angles
No; they do not have congruent corresponding angles
Yes; they have proportional corresponding sides
No; they do not have proportional corresponding sides
Yes; they have congruent corresponding angles
No; they do not have congruent corresponding angles
Yes; they have proportional corresponding sides
No; they do not have proportional corresponding sides
2 answers:
Answer: No; they do not have proportional corresponding sides
Step-by-step explanation:
Since, here in triangles GHI and JKL,
∠ G = 46°, ∠I = 27° ⇒ ∠H = 107° , ∠L = 27°, ∠ K = 108°⇒∠J = 45°
GH = 4, HI = 5 , KJ= 2 and JL = 4
Here ∠I ≅ ∠L
But,
Therefore, they do not have proportional corresponding sides.
That is why they are not similar to each other.
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The slide needs to be 4.123 meters
Step-by-step explanation:
Length for the ladder- 1 mtr
Distance of the bottom of the slide from the ladder- 4 mtr
Length of the slide needed
We can view the whole set up in the form of a right-angled triangle with the base representing the slide distance from the ladder, ladder length representing altitude and slide length representing as hypotenuse (As provided in the diagram)
For right-angled triangle we know from Pythagoras theorem-
Base² + altitude²= hypotenuse ²
Substituting the values of base as 4 mtr and altitude as 1 m
(Hypotenuse)²= 17
∴ Hypotenuse (slide length) =4.123 mtr
∴ Length of the slide needed= 4.123 meters
