Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.

lwfrgin
2020-12-16
Answered

Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.

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Brittany Patton

Answered 2020-12-17
Author has **100** answers

Step 1

To make the triangle congruent by using the SAS congruence,

First naming the edges and vertex of the triangle,

Step 2

By using sum of interior angle property in

it is given that,

Adding equation (i) and (ii) and subtracting them form

Now, in

AB=EF(given)

BC=DE(given)

Yes, the provided information is enough to prove the triangle congruent by SAS.

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I want to understand how Schnass $\u2020$ arrived at the maximising objective as described below

$\begin{array}{rl}{\displaystyle \underset{D,A}{min}\Vert X-DA{\Vert}_{F}^{2}}& =\underset{D}{min}\sum _{n}\underset{|I|\le S}{min}\Vert {x}_{n}-{D}_{I}{D}_{I}^{\u2020}{x}_{n}{\Vert}_{2}^{2}\\ & =\Vert X{\Vert}_{F}-\underset{D}{max}\sum _{n}\underset{|I|\le S}{max}\Vert {D}_{I}{D}_{I}^{\u2020}{x}_{n}{\Vert}_{2}^{2}\end{array}$

where $\u2020$ is the pseudo-inverse, $S$ denotes the cardinality of column vectors an of matrix $A$.

$\begin{array}{rl}{\displaystyle \underset{D,A}{min}\Vert X-DA{\Vert}_{F}^{2}}& =\underset{D}{min}\sum _{n}\underset{|I|\le S}{min}\Vert {x}_{n}-{D}_{I}{D}_{I}^{\u2020}{x}_{n}{\Vert}_{2}^{2}\\ & =\Vert X{\Vert}_{F}-\underset{D}{max}\sum _{n}\underset{|I|\le S}{max}\Vert {D}_{I}{D}_{I}^{\u2020}{x}_{n}{\Vert}_{2}^{2}\end{array}$

where $\u2020$ is the pseudo-inverse, $S$ denotes the cardinality of column vectors an of matrix $A$.

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