10.04 Similar triangle tests
State whether the following pairs of triangles are similar, and if so, state the similarity test that proves this.
For each of the following sets of triangles:
Identify which two are similar.
Identify the similarity test that the pair satisfy: AAA, SSS, SAS, or RHS.
Consider the following diagram:
Identify two similar triangles and state the similarity test that they satisfy.
Given that DE = 7, what is the length of BC?
Consider the following diagram:
State the similarity test that triangles \triangle ABX and \triangle CDX satisfy.
Given that AB = 5, what is the length of CD?
Consider the following diagram:
Identify two similar triangles and state the similarity test that they satisfy.
Given that KL = 20, what is the length of MN?
Consider the following diagram, where AD is a straight line:
What information is required to know that triangles \triangle ABC and \triangle DBE are in fact similar?
Consider the following diagram, where EH and FG are straight lines:
What information is required to know that triangles \triangle EFX and \triangle GHX are in fact similar?
Consider the following diagram, where TZ and UY are non-parallel straight lines:
Explain why the triangles \triangle TUX and \triangle YZX are not similar.
Peter constructs a ramp in the shape of a right-angled triangle. To give the ramp more strength, he wants to place a brace from the base point across to the hypotenuse. The brace should meet the hypotenuse at a right angle, as shown in the diagram:
State the similarity test that the triangles \triangle ABC and \triangle ADB satisfy.
How long does the brace, BD, need to be?
Hence, find the length x.
A horizontal brace lies between the slanted sides of an A-shaped ladder. In this position, the top of the ladder is 220 \text{ cm} from the ground. The brace is 44 \text{ cm} in length, and sits 71 \text{ cm} from the top of the ladder.
How far apart are the feet of the ladder? Round your answer to the nearest whole centimetre.
A large tree casts a shadow of 30\text{ m}. At the same time, a 2\text{ m} high stick, standing vertically, casts a shadow of 3\text{ m}.
State the reasons why the triangles \triangle ABE and \triangle DCE are similar.
If the height of the tree is h metres, find h.