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Give an example of how similar triangles can be used in real-world applications.
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One example is calculating the height of a tree using its shadow and a stick's shadow by forming proportions between the corresponding sides of the triangles.
What is the formula to find the height of a tree using similar triangles, given the lengths of the shadows and a stick height?
Height of the tree = (Height of stick / Length of stick's shadow) * Length of tree's shadow
Define similar triangles.
Triangles that have the same shape but not necessarily the same size. Corresponding angles have the same measure and corresponding sides are proportional.
If two triangles have side ratios of 3:2, what must the ratio of their other corresponding sides be?
The ratio of the other corresponding sides must also be 3:2.
How do you determine the unknown angle in a triangle if two angles are given?
Subtract the sum of the two given angles from 180°.
In similar triangles, if corresponding sides are proportional at 2:1, what are the ratios of the sides of the triangles?
The ratios of all corresponding sides will be 2:1.
How do you verify triangle similarity using the Side-Side-Side (SSS) criterion?
Check that the ratios of all three pairs of corresponding sides are equal.
Given triangles with sides in the ratio 9:6 and 15 on the larger triangle, what is the corresponding side length on the smaller triangle?
The corresponding side length on the smaller triangle is 10 (since 15 * 6 / 9 = 10).
What needs to be true for triangles to be similar using the Angle-Angle-Angle (AAA) criterion?
All three pairs of corresponding angles must be congruent.
What are the conditions for a triangle to be congruent?
Corresponding sides must have the same length and corresponding angles must be congruent.
How can you use the Side-Angle-Side (SAS) criterion to prove triangles are similar?
By showing two pairs of corresponding sides are proportional and the included angles are congruent.
What angles in two similar triangles would be congruent given angles D = 35° and F = 43°?
Angles C = 43° and A = 35° in the other triangle.
Using similar triangles, how do you find the length of the side when the proportional ratios are given?
Set up a proportion using the known sides and solve for the unknown side.
How does the sum of angles in a triangle help determine similarity?
If two corresponding angles are known to be congruent, the third pair must also be congruent because the sum of angles in a triangle is always 180°.
What is the Angle-Angle (AA) criterion for triangle similarity?
Two pairs of corresponding angles are congruent, which implies the third pair of angles is also congruent, making the triangles similar.
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