Show Learn more about Basics (types, similarity, etc) Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you Elementary Geometry For College Students, 7e Author:Alexander, Daniel C.; Koeberlein, Geralyn M. Elementary Geometry for College Students Author:Daniel C. Alexander, Geralyn M. Koeberlein Publisher:Cengage Learning Elementary Geometry For College Students, 7e ISBN:9781337614085 Author:Alexander, Daniel C.; Koeberlein, Geralyn M. Publisher:Cengage, Elementary Geometry for College Students ISBN:9781285195698 Author:Daniel C. Alexander, Geralyn M. Koeberlein Publisher:Cengage Learning
There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL. 1. SSS (side, side, side)SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. For example:
(See Solving SSS Triangles to find out more)
If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. 2. SAS (side, angle, side)SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal. For example:
(See Solving SAS Triangles to find out more)
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent. 3. ASA (angle, side, angle)ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal. For example:
(See Solving ASA Triangles to find out more)
If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent. 4. AAS (angle, angle, side)AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal. For example:
(See Solving AAS Triangles to find out more)
If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent. 5. HL (hypotenuse, leg)This one applies only to right angled-triangles!
HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs") It means we have two right-angled triangles with
It doesn't matter which leg since the triangles could be rotated. For example:
(See Pythagoras' Theorem to find out more)
If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent. Caution! Don't Use "AAA"AAA means we are given all three angles of a triangle, but no sides. This is not enough information to decide if two triangles are congruent! Because the triangles can have the same angles but be different sizes:
Without knowing at least one side, we can't be sure if two triangles are congruent. Copyright © 2017 MathsIsFun.com |