Similar Triangles (Grade 10)

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Similar Triangles

A triangle where [math]ang B = 30°[/math] will be similar to a triangle where [math]ang C = 60°.[/math]
Right Triangle ABC v1

Always
If the side lengths are the same
If they are right triangles
Never

Matt is flying a kite and measures the angle of his string to the ground as 30 degrees. Samantha is also flying a kite using a string which is 150 feet long. Her kite is at an altitude of 75 feet. Are the two triangles formed by Matt's and Samantha's kite strings to the ground similar? Show your work.
Right Triangle ABC v3

If no side lengths are known, two triangles can be proven to be similar as long as at least angles are known.

Triangle 1: A = 105, B = 25
Triangle 2: B = 25, C = 50
These 2 triangles are similar.
Scalene Triangle ABC v1

True
False

Are these two triangles are similar?
Triangle 1: A = 125, C = 18
Triangle 2: B = 125, C = 35
Acute Triangle ABC v1

Yes, the triangles are similar.
No, the triangles are not similar.

Are these two triangles similar?
Triangle ABC: [math]ang A=28°, ang B=91° [/math]
Triangle DEF: [math]ang D=28°, ang E=61° [/math]

Yes, the triangles are similar.
No, the triangles are not similar.

Chad is using a ladder that is 10 feet long while Sam is using a ladder 15 feet long. Chad's ladder reaches 7 feet up the wall and Sam's ladder reaches 10 feet up the wall. Do both ladders form similar triangles with the wall and ground?
Show your work.

Two airplanes are approaching an airport to land. The pilot in plane A records an angle of descent of 15 degrees for her plane. A person near the runway finds the angle of elevation to plane B to be 15 degrees. Are the two planes descending at the same angle? Sketch a diagram and show your work.

Jennifer leaves her house walking in a direction 20 degrees East of North and walks for 20 minutes. She then walks 30 degrees South of East for 50 minutes at the same pace.
Tara goes for a jog and leaves home in a direction 60 degrees West of North. After 10 minutes she heads 70 degrees South of West for 25 minutes at the same pace.
If both Jennifer and Tara return straight home, will their paths form similar triangles?
Show your work.