Conditions for Similarity of Two Triangles
- If their corresponding angles are equal.
- If their corresponding sides are in the same proportion/ratio.
What is the criterion for similarity of two triangles?
The Side-Angle-Side (SAS) criterion for similarity of two triangles states that “If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar”.
What is the AA criterion for similarity?
The Angle-Angle (AA) criterion for similarity of two triangles states that “If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar”.
What is the most important property of a triangle?
A triangle has three sides and three angles. The most important property of a triangle is the sum of the interior angles of a triangle is equal to 180°. In this article, let us discuss the important criteria for the similarity of triangles with its theorem and proof and many solved examples.
What is the AA criterion?
The AA criterion states that if two angles of a triangle are respectively equal to the two angles of another triangle, we can prove that the third angle will also be equal on both the triangles. This can be done with the help of the angle sum property of a triangle.
What is the line PQ parallel to?
Consider the same figure as given above. It is observed that DP/PE = DQ/QF and also in the triangle DEF, the line PQ is parallel to the line EF.
Which triangles are always similar?
Equilateral triangles are always similar. Any two equilateral triangles are always similar irrespective of the length of the sides of the equilateral triangle. Two isosceles right triangles are also always similar.
What is similar triangle?
Introduction to Similar Triangles. Similar triangles are the triangles that look similar to each other but not exactly the same. Two triangles will be similar if the angles are equal ( corresponding angles) and sides are in the same ratio or proportion ( corresponding sides ). Similar triangles may have different individual lengths of the sides ...
What is the SSS similarity criterion?
According to the SSS similarity criterion, two triangles will the similar to each other if the corresponding ratio of all the sides of the two triangles are equal. This criterion is commonly used when we only have the measure of the sides of the triangle and have less information about the angles of the triangle.
What is the AA similarity rule?
AA similarity criterion tells us that if any two angles in a triangle are respectively equal to any two angles of another triangle, then they must be similar triangles. AA similarity rule is easily applied when we only know the measure of the angles and have no idea about the length of the sides of the triangle.
What happens if two triangles are similar?
If two triangles are similar or proved similar by any of the above-stated criteria, then they possess few properties of the similar triangles. Properties of similar triangles are given below:
How to find missing sides of a triangle?
Missing sides of a similar triangle can find out by comparing the ratio of the consecutive corresponding sides of the triangle. We compare the ratios and find the length of the unknown side of the triangle.
When are two sides of a triangle similar?
According to the SAS similarity criterion, if any two sides of the first triangle are in exact proportio n to the two sides of the second triangle along with the angle formed by these two sides of the individual triangles are equal, then they must be similar triangles. This rule is generally applied when we only know the measure of two sides and the angle formed between those two sides in both the triangles respectively.
Which pair of angles must be congruent?
By Third Angle Theorem, the third pair of angles must also be congruent.
What are the angles of ABC and ADE?
In triangles ABC and ADE, we have. ∠B and ∠D are right angles. ∠A is common angle. Two angles of one triangle are congruent to two angles of another triangle. By Third Angle Theorem, the third pair of angles must also be congruent. So, the triangles ABC and ADE are similar triangles.
Is ABC a similar triangle to DEF?
So, the triangles ABC and DEF are not similar triangles.
