What is the difference between SSA and SAS?

Asked By: Aizhu Swasza | Last Updated: 19th June, 2020
Category: science space and astronomy
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Both of these two postulates tell you that you have two congruent sides and one congruent angle, but the difference is that in SAS, the congruent angle is the one that is formed by the two congruent sides (as you see, the "A" is between the two S), whereas with SSA, you know nothing about the angle formed by the two

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Subsequently, one may also ask, how do you tell if a triangle is SAS or SSA?

SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal. 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.

Additionally, is SSA a congruence shortcut? Four shortcuts allow students to know two triangles must be congruent: SSS, SAS, ASA, and AAS. Knowing only side-side-angle (SSA) does not work because the unknown side could be located in two different places.

Keeping this in consideration, what is the difference between AAS and ASA?

While both are the geometry terms used in proofs and they relate to the placement of angles and sides, the difference lies in when to use them. ASA refers to any two angles and the included side, whereas AAS refers to the two corresponding angles and the non-included side.

Is there an SSA congruence?

Same as the Angle Side Side Postulate (ASS) If two triangles have two congruent sides and a congruent non included angle, then triangles are NOT NECESSARILLY congruent. This is why there is no Side Side Angle (SSA) and there is no Angle Side Side (ASS) postulate.

28 Related Question Answers Found

How many congruence rules are there?

There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

What is SSS ASA SAS in math?

SSS (side-side-side) All three corresponding sides are congruent. SAS (side-angle-side) Two sides and the angle between them are congruent. ASA (angle-side-angle)

How do you prove the SAS congruence theorem?

SAS Postulate (Side-Angle-Side) If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

How do you prove in SAS?

You can prove that triangles are similar using the SAS~ (Side-Angle-Side) method. SAS~ states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are congruent.

What does it mean to be congruent?


The adjective congruent fits when two shapes are the same in shape and size. If you lay two congruent triangles on each other, they would match up exactly. Congruent comes from the Latin verb congruere "to come together, correspond with." Figuratively, the word describes something that is similar in character or type.

What is SAS congruence rule?

The Side Angle Side postulate (often abbreviated as SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

Is AAA a congruence theorem?

(Video) Congruent Triangles AAA
Here is a video demonstrating why AAA is NOT a valid congruence rule. As you can see in the video, triangles that have 3 pairs of congruent angles do not necessarily have the same size. AAA (Angle-Angle-Angle) is not a congruence rule!

Does ASA prove similarity?

Two triangles are similar if and only if the corresponding sides are in proportion and the corresponding angles are congruent. Just as there are specific methods for proving triangles congruent (SSS, ASA, SAS, AAS and HL), there are also specific methods that will prove triangles similar.

Why do we study congruence?

For two polygons to be congruent, they must have exactly the same size and shape. This means that their interior angles and sides must all be congruent. That's why studying the congruence of triangles is so important--it allows us to draw conclusions about the congruence of polygons, too.

Can congruence be proven by AAS?


The "non-included" side in AAS can be either of the two sides that are not directly between the two angles being used. Once triangles are proven congruent, the corresponding leftover "parts" that were not used in SSS, SAS, ASA, AAS and HL, are also congruent.

What is ASA theorem?

ASA Theorem (Angle-Side-Angle)
The Angle Side Angle Postulate (ASA) says triangles are congruent if any two angles and their included side are equal in the triangles. An included side is the side between two angles.

What is Cpctc Theorem?

CPCTC is an acronym for corresponding parts of congruent triangles are congruent. CPCTC is commonly used at or near the end of a proof which asks the student to show that two angles or two sides are congruent. Corresponding means they're in the same position in the 2 triangles.

What is a ASA triangle?

"ASA" means "Angle, Side, Angle" "ASA" is when we know two angles and a side between the angles. To solve an ASA Triangle. find the third angle using the three angles add to 180° then use The Law of Sines to find each of the other two sides.

Why is SSA an ambiguous case?

The “Ambiguous Case” (SSA) occurs when we are given two sides and the angle opposite one of these given sides. The triangles resulting from this condition needs to be explored much more closely than the SSS, ASA, and AAS cases, for SSA may result in one triangle, two triangles, or even no triangle at all!

Why does SSA work in right triangles?


Hypotenuse-Leg (HL) for Right Triangles. There is one case where SSA is valid, and that is when the angles are right angles. Using words: In words, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.

Is SSA a similarity theorem?

SSA theorem
Two triangles are similar if the lengths of two corresponding sides are proportional and their corresponding angles across the larger of these two are congruent.

Is AAA a postulate?

In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent. (This is sometimes referred to as the AAA Postulate—which is true in all respects, but two angles are entirely sufficient.) The postulate can be better understood by working in reverse order.