Is Ssa A Congruence Theorem

SSA Congruence Rule

SSA congruence rule is also known as side-side-bending congruence rule refers to the congruence of two triangles. Ii triangles are said to be congruent when it ane of these five conditions are met, SSS, SAS, ASA, AAS, and RHS criteria. SSA congruence rule states that if 2 sides and an angle not included between them are respectively equal to two sides and an bending of the other then the two triangles are equal. Nevertheless, this congruence or criterion is not valid. Let us see why it is non and detect proof for it.

1.	What is the SSA Congruence Rule?
2.	Proof of SSA Congruence Rule
three.	FAQs on SSA Congruence Rule

What is the SSA Congruence Rule?

The SSA congruence rule states that if two sides and an angle not included between them are respectively equal to two sides and an angle of the other then the 2 triangles are equal. Nevertheless, with this congruence rule, two triangles are non said to be congruent since the sides of the 2 triangles may not be on the same corresponding sides. Both the triangles might finish upwardly having different shapes and sizes from each other. Thus, the SSA congruence rule is not valid.

Proof of SSA Congruence Rule

As we already learned that this congruence rule is not valid and triangles cannot be coinciding, let united states run into the reasons as to why SSA will not piece of work. Consider the following effigy:

SSA Congruence Rule

In the 2 triangles ∆ABC and ∆DEF, we have AB = DE, BC = EF, and ∠C = ∠F (non-included angles). We meet that fifty-fifty though two pairs of sides and a pair of angles are (correspondingly) equal, the two triangles are not congruent. The two triangles do not accept the same shape and size. Therefore, the SSA congruence rule is not valid.

Let u.s.a. consider an example to understand this amend. Suppose that there is a triangle two of whose sides accept lengths 4cm and 3cm, and a non-included angle is 30°. Let'south try to geometrically construct such a triangle. If during our construction process, we find that we can construct only one (unique) such triangle, so SSA congruence would be valid, but on the other paw, if nosotros find that we can construct more i such triangle, and then SSA congruence would exist invalid because then ii different triangles can accept the same ii lengths and a non-included angle.

Here'due south a step-by-step construction:

Step i: Construct BC = 4cm.

Pace two: Through C, draw a ray CX such that ∠BCX = 30°

SSA Congruence Rule

Step iii: Take a point A on the ray CX such that AB = 3cm. How many locations of A are possible? Configure the compass such that the altitude between its tip and the pencil's tip is 3cm. Place the tip of the compass on B such that two points can be marked off on CX as shown in the image below.

SSA Congruence Rule

Thus, ii different triangles have been successfully constructed i.eastward. ∆A₁BC and ∆A₂BC with a pair of sides and a not-included bending. This means 2 things:

A pair of sides and a non-included angle will not uniquely decide a triangle. In other words, congruence through SSA is invalid.
A pair of sides and the included angle volition uniquely make up one's mind a triangle. In other words, congruence through SAS is valid.

Therefore, it is proved that the SSA congruence rule is not valid.

Examples on SSA Congruence Dominion

Example 1: Triangle ABC is an isosceles triangle and the line segment Advertizement is the angle bisector of the angle A. Can you bear witness that ΔADB is congruent to the ΔADC by using SAS dominion?

Solution:

The triangle, ABC is an isosceles triangle where it is given that AB=Air conditioning. Now the side AD is common in both the triangles ΔADB and ΔADC. Equally the line segment Ad is the angle bisector of the angle A then information technology divides the ∠A into 2 equal parts. Therefore, ∠BAD=∠CAD. Now according to the SAS dominion, the 2 triangles are congruent. Hence, ΔADB≅ΔADC.
Example 2: Prove that △ACF≅△AEB, if ∠C=∠E and AC=AE.

Solution:

Hither,

∠C=∠E (given)

Air-conditioning=AE (given)

∠A=∠A (common)

Therefore, Δ ABD ≅ Δ ACD (ASA rule)

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Practice Questions on SSA Congruence Rule

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FAQs on SSA Congruence Rule

What is Meant past SSA Congruence Rule?

SSA congruence rule states that if two sides and an bending not included between them are respectively equal to two sides and an angle of the other so the two triangles are equal. However, this congruence or benchmark is not valid.

Why is SSA Congruence Rule not Possible?

The SSA congruence rule is not possible since the sides could be located in ii different parts of the triangles and not corresponding sides of two triangles. The size and shape would be different for both triangles and for triangles to be congruent, the triangles need to be of the same length, size, and shape.

When Can SSA Show Triangles are Congruent?

SSA congruence rule can testify if triangles are congruent in two scenarios:

If three sides of a triangle are coinciding to three sides of some other triangle, the triangles are considered congruent. (SSS Congruence Rule).
If ii sides and the included angle of one triangle are congruent to the respective parts of the other triangle, the triangles are considered coinciding. (SAS Congruence Dominion).

Is SSA a Criterion for Congruence of Triangles?

No, the SSA congruence rule is not a valid criterion that proves if two triangles are congruent to each other.

Does SSA Piece of work in Right Angle Triangle?

One of the cases the SSA congruence rule might work is in right angle triangles where the angles are at right angles. The condition for this to exist possibly valid is if the hypotenuse and a leg of one correct triangle are congruent to the hypotenuse and a leg of a 2d right triangle, then the triangles are congruent.

What is SSS, SAS, ASA, and AAS?

The 4 different triangle congruence theorems are:

SSS(Side-Side-Side): Where iii sides of two triangles are equal to each other.
SAS(Side-Angle-Side): Where two sides and an angle included in between the sides of ii triangles are equal to each other.
ASA(Angle-Side-Angle): Where two angles forth with a side included in between the angles of whatever two triangles are equal to each other.
AAS(Angle-Angle-Side): Where two angles of whatsoever two triangles along with a side that is not included in betwixt the angles, are equal to each other.

Why SSA is Not a Postulate?

SSA is not a postulate because two sides and a non-included angle do non guarantee the triangles to be congruent. The sides could be of any length and at different locations.