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In order for 2 triangles to be congruent, it must be true that each pair of corresponding sides are congruent (equal in length) and each pair of corresponding angles are congruent (equal in size).
It is not necessary to prove that all three pairs of sides and all three pairs of angles are congruent. If you prove that all the sides are congruent, then the angles must be congruent, too. This is known as SSS, the side-side-side method of proving congruency.
There a four basic ways to prove congruency. They are:
1. SSS (side-side-side) Prove that all three pairs of sides are equal in length.
2. SAS (side-angle-side) Prove that two sides and the angle between them are equal.
3. ASA (angle-side-angle) Prove that two angles and the side between them are equal.
4. AAS (angle-angle-side) Prove that two angles and a side that is NOT between them are equal.
Note that you cannot prove that triangles are congruent with AAA or SSA.
Note: for right triangles we can use HL. This is a special method that just looks at the hypotenuse and the leg of one triangle and compares it to the hypotenuse of the other. However, if they are both right triangle, the angle between the hypotenuse and the leg is a right angle so this is really just a special case of AAS that we can only use for right triangles.
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Why can't you use AAA to prove two triangles congruent?
You can't use AAA to prove two triangles congruent because triangles can have the same measures of all its angles but be bigger or smaller, AAA could probably be used to prove two triangles are similar not congruent.
What are three ways that you can prove that triangles are congruent?
If triangles have the corresponding sides congruent then they are congruent. SSS If two triangles have two sides and an included angle congruent then they are congruent. SAS If two triangles have two angles and an included side congruent then they are congruent. ASA SSA doesn't work.
what- If you are given or can prove that two triangles are congruent, then you may use CPCTC to prove that the angles or sides are?
congruent
Which explains why AAA is not enough to prove two triangles congruent?
Two triangles with three congruent angles may have different side lengths.
Which condition does not prove two triangles are congruent?
The colours of their sides.
Why can't you use AAA to prove two triangles congruent?
You can't use AAA to prove two triangles congruent because triangles can have the same measures of all its angles but be bigger or smaller, AAA could probably be used to prove two triangles are similar not congruent.
What are three ways that you can prove that triangles are congruent?
If triangles have the corresponding sides congruent then they are congruent. SSS If two triangles have two sides and an included angle congruent then they are congruent. SAS If two triangles have two angles and an included side congruent then they are congruent. ASA SSA doesn't work.
How can you use SSS with CPCTC?
You can prove that to triangles are congruent with SSS, then use CPCTC to prove that two corresponding angles of those triangles are congruent.
How would you prove triangles are congruent?
You could prove two triangles are congruent by measuring each side of both triangles, and all three angles of each triangle. If the lengths of the sides are the same, and so are the angles, then the triangles are congruent... if not, then the triangles are not congruent. If the triangles have the exact same size and shape then they are congruent.
what- If you are given or can prove that two triangles are congruent, then you may use CPCTC to prove that the angles or sides are?
congruent
How does sas theorem answer?
The SAS theorem is used to prove that two triangles are congruent. If the triangles have a side-angle-side that are congruent (it must be in that order), then the two triangles can be proved congruent. Using this theorem can in the future help prove corresponding parts are congruent among other things.
Which explains why AAA is not enough to prove two triangles congruent?
Two triangles with three congruent angles may have different side lengths.
Which condition does not prove two triangles are congruent?
The colours of their sides.
What postulate or theorem verifies the congruence of triangles?
sssThere are five methods for proving the congruence of triangles. In SSS, you prove that all three sides of two triangles are congruent to each other. In SAS, if two sides of the triangles and the angle between them are congruent, then the triangles are congruent. In ASA, if two angles of the triangles and the side between them are congruent, then the triangles are congruent. In AAS, if two angles and one of the non-included sides of two triangles are congruent, then the triangles are congruent. In HL, which only applies to right triangles, if the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent.
Prove that the diagonals of rectangle are equal?
prove any two adjacent triangles as congruent
How do you prove something is congruent with the form SAS?
Show that, if you have two triangles, two of the sides and the angle in between are congruent.
Which arrangement cannot be used to prove two triangles congruent?
SSA
