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because neither side congruency nor angle congruency can be proved... to put it simply, this is because there would be too many variables with too little information if you set it up in an equation OR the fact that nothing is sandwiched between 2 parts like a side is not put between a side and an angle or vice versa, etc. In geometry class, we call this the "donkey theorem" (hence the acronym Angle Side Side)
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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.
Ssa sas sss which of these mean congruent?
SAS and SSS are congruent. SSA need not be.
How you can prove that two triangles are congruent?
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.
What is ass or ssa congruence postulate?
The ASS postulate would be that:if an angle and two sides of one triangle are congruent to the corresponding angle and two sides of a second triangle, then the two triangles are congruent.The SSA postulate would be similar.Neither is true.
Why AA and SSA are no valid methods to prove triangles congruent?
Because you need information about all three parts of the triangle, either the side or the angle opposite it, for each of the sides of a triangle. In AA you are missing the third angle, you could have a triangle where both angles were the same but the height could be different giving you a taller or shorter triangle. In SSA, the angle would be the one opposite the first side, so you have no information about the third side
Which arrangement cannot be used to prove two triangles congruent?
SSA
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.
Is ssa a conguent theorem or postulate?
No. SSA can give rise to a pair of non-congruent triangles.
Is it true triangles satisfying SSA are congruent?
No. SSA is ambiguous. Unless A = 90 degrees, there are two possible configurations for the triangle. So they need not be congruent.
Why does the SSA postulate work only with the right triangle?
You can't use SSA or ASS as a postulate because it doesn't determine that the triangles are congruent; right triangles are most likely determined by HL: hypotenuse leg- genius!
If one pair of opposite angles and one pair of opposite sites of a quadrilateral is congruent then the quadrilateral is a parallelogram. How can it be proven?
draw a diagonal through opposite corners of the quadrilateral. This makes two triangles. Prove the triangles are congruent using SSA (side side angle) congruence. Then show that the other two sides of the quadrilater must be congruent to each other, so it is a parallelogram.
Ssa sas sss which of these mean congruent?
SAS and SSS are congruent. SSA need not be.
How you can prove that two triangles are congruent?
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.
Why is SSA not a congruent shortcut?
SSA is ambiguous. If A is not a right angle, then there are two possible configurations for the triangle. So they need not be congruent.
SSA side-side-angle guarantees congruence between two triangles?
trueTrue -- SSA does NOT guarantee congruence.Only SAS, SSS, and ASA can do that (and AAS, because if two pairs of corresponding angles are congruent, the third has to be).
What is ass or ssa congruence postulate?
The ASS postulate would be that:if an angle and two sides of one triangle are congruent to the corresponding angle and two sides of a second triangle, then the two triangles are congruent.The SSA postulate would be similar.Neither is true.
Why AA and SSA are no valid methods to prove triangles congruent?
Because you need information about all three parts of the triangle, either the side or the angle opposite it, for each of the sides of a triangle. In AA you are missing the third angle, you could have a triangle where both angles were the same but the height could be different giving you a taller or shorter triangle. In SSA, the angle would be the one opposite the first side, so you have no information about the third side
