Kuta Software Infinite Geometry Similar Right Triangles (2024)

FAQs

How do you prove triangles similar answers? ›

AA (Angle-Angle): If triangles have two of the same angles, then the triangles are similar. SAS (Side-Angle-Side): If triangles have two pairs of proportional sides and equal included angles, then the triangles are similar.

If the lengths of the hypotenuse and a leg of a right triangle are proportional to the corresponding parts of another right triangle, then the triangles are similar. (You can prove this by using the Pythagorean Theorem to show that the third pair of sides is also proportional.)

Right Triangle Similarity Theorem

Given a right triangle, if an altitude is drawn from the vertex of the right angle to the hypotenuse, then the two triangles formed are similar to the original triangle and to each other.

Two triangles are similar if their corresponding angles are congruent. Therefore, knowing the measure of two angles in each triangle is sufficient to determine if the triangles are similar.

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar. Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ. Also, read: Isosceles Triangle Equilateral.

Similar Right triangles: Two right triangles are similar if the corresponding sides are proportional to each other, and the corresponding angles are congruent.

0 energy points. A 45-45-90 triangle is a special type of right triangle, where the ratio of the lengths of the sides of a 45-45-90 triangle is always 1:1:√2, meaning that if one leg is x units long, then the other leg is also x units long, and the hypotenuse is x√2 units long.

Solving right triangles

We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts. Pythagorean theorem: a² + b² = c². Sines: sin A = a/c, sin B = b/c. Cosines: cos A = b/c, cos B = a/c.

The triangle similarity theorems, which are Angle - Angle (AA), Side - Angle - Side (SAS) and Side - Side - Side (SSS), serve as shortcuts for identifying similar triangles.

What is the longest side in a right triangle? ›

The hypotenuse is always the longest side in a right triangle because it is opposite of the largest angle, the ninety degree angle.

Each term of a geometric sequence is formed by multiplying the previous term by a constant number r, starting from the first term a1. Therefore, the rule for the terms of a geometric sequence is an=a1(r)^(n-1).

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar. It is sufficient to prove that only two pairs of angles are respectively equal to each other.

This theorem can be proved by taking two triangles such as ABC and DEF (Refer to the same figure as given above). In the triangle DEF, the line PQ is parallel to EF. So, ∆ ABC ≅ ∆ DPQ. Hence, we can say ∠A = ∠D, ∠B=∠P and ∠C= ∠Q, which means that the triangle ABC is similar to the triangle DEF.

SAS or Side-Angle-Side Similarity

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar. Thus, if ∠A = ∠X and AB/XY = AC/XZ then ΔABC ~ΔXYZ.