Is there an analog to the SSS triangle congruence theorem for quadrilaterals?

Is there an analog to the SSS triangle congruence theorem for quadrilaterals?

Question
Congruence
asked 2020-10-23
Is there an analog to the SSS triangle congruence theorem for quadrilaterals?

Answers (1)

2020-10-24
Step 1
To show whether there is an analog to the SSS triangle congruence theorem for quadrilateral.
Step 2
The SSS triangle congruence theorem states that if all 3 sides of one triangle are in proportion to all 3 sides of another triangle then those triangles are similar.
Step 3
It is observed that Side-Side-Side congruence is not sufficient to prove that two quadrilaterals are congruent. Since there are 4 parameters for a quadrilateral SSSS is possible.
Step 4
Therefore, there is no analog to the SSS triangle congruence theorem for quadrilateral.
0

Relevant Questions

asked 2020-12-06
With of the following triangle congruence shortcuts could be used to prove PRQ = TRS

Given Data,
\(\displaystyle\angle{Q}\stackrel{\sim}{=}\angle{S}\)
\(\displaystyle\overline{{{Q}{R}}}\stackrel{\sim}{=}\overline{{{S}{R}}}\)
a)Side-Side-Side Postulate (SSS)
b)Side-Angle-Side Postulate (SAS)
c)Angle-Side-Angle Postulate (ASA)
d)Angle-Angle-Side Theorem (AAS)
asked 2020-11-08
Select all statements that are true about the triangles.

-Triangle ABC and DCB are congruent by the Angle-Angle Triangle Congruence theorem.
-Triangle ABC and BCD are congruent by the Angle-Side-Angle Triangle Congruence theorem.
-Triangle ABC and BCD are congruent by the Side-Side-Side Triangle Congruence theorem.
-Triangle ABC and DCB are congruent by the Side-Angle-Side Triangle Congruence theorem.
-Triangle ABC and DCB are congruent by the Side-Side-Side Triangle Congruence theorem.
-There is not enough information to determine if the triangles are congruent.
asked 2021-04-17
Solve the following congruence.
\(\displaystyle{x}^{{{2}}}\equiv{7}\pm{o}{d}{29}\)
asked 2021-02-25
Find the triangle congruence (SSS SAS AAS HL)

Given: bar(SQ) and bar(PR) bisect each other.
asked 2021-04-25
To determine:The check digit of an ISSN that has these initial 7 digits 1553-734
asked 2021-04-13
To find:
The smallest the smallest positive integer such that if we divide it by two, three and four, the remainder is one but seven divides the number evenly.
asked 2021-05-06
To find:
The smallest positive integer such that if we divide it by three, the remainder is 2. if we divide it by five, the remainder is 3. if we divide it by seven, the remainder is 2.
asked 2021-01-30
In congruence classes \(\displaystyle\frac{{Z}}{{{m}{Z}}}\), reduce the equation \(\displaystyle{a}_{{m}}\cdot{{x}_{{m}}^{{2}}}={c}_{{m}}\) either by finding convenient representation for \(\displaystyle{a}_{{m}}{\quad\text{and}\quad}{b}_{{m}}\) or by using the inverse of \(\displaystyle{a}_{{m}}\). Then find a solution for this congruence directly or by replacing \(\displaystyle{c}_{{m}}\) : with its appropriate representative in \(\displaystyle\frac{{Z}}{{{m}{Z}}}\). If there is no solution explain why. Here \(\displaystyle{a}_{{m}},{b}_{{m}},{x}_{{m}}{\left(={x}\right)},{c}_{{m}}\in\frac{{Z}}{{{m}{Z}}}:\)
\(\displaystyle{I}{n}\frac{{Z}}{{{19}{Z}}},{\left[{2}\right]}\cdot{x}^{{2}}={\left[{13}\right]}:\)
asked 2021-02-13
decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.
asked 2020-12-16
Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.
...