Determine the unknown sides or angles of the given congruent triangles.

Question

Shasha14 · Answer

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Extrinix · Answer

QUESTION 1: $DEN \cong YAF$

we can find our similar angles easily by seperating the congruency statement out,
$D=Y$ , $E=A$ , $N=F$
We already have D and Y so we can skip those

now we have $E$ and $A$
$m \angle E = 102 ^ \circ$ 
E being equal to A makes this statement true:
$m \angle A = 102 ^ \circ$

now to find $N=F$,
we know that the inside angles of a triangle must always equal 180 so we make an equation to find out what $N$ is:
$n+32 ^\circ +102 ^\circ =180 ^\circ$   combine like terms
$n+134 ^\circ = 180 ^\circ$   remove 134 from both sides
$n = 46 ^\circ$    N equals 46, making F equal 46

Extrinix · Answer

QUESTION 2: $ABC \cong FED$

now this one is a little bit different, this one you are finding the sides not the angles
so we must figure out which sides match which:
$\overline{AB}=\overline{FE}$ , $\overline{BC}=\overline{ED}$ , $\overline{CA}=\overline{DF}$

lets start with $\overline{AB}=\overline{FE}$
it says that $\overline{AB}=4.2$ meaning $\overline{FE}=4.2$ by congurence.

now to find $\overline{BC}=\overline{ED}$
it says that $\overline{ED}=5$ so that makes $\overline{BC}=5$ by congruence

now $\overline{CA}=\overline{DF}$
for this one it gives$\overline{AD}$ and $\overline{DC}$
add these together $4+3$ and that gives you $\overline{CA}=7$
meaning $\overline{DF}=7$ by congruence

there's your info for #2

Extrinix · Answer

QUESTION 3: $BCN \cong NSB$

so to start off note that this question is similar to #2, finding sides
$\overline{BC}=\overline{NS}$ , $\overline{CN}=\overline{SB}$ , $\overline{NB}=\overline{BN}$

now lets figure out $\overline{BC}=\overline{NS}$
it says $\overline{NS}=2$ meaning $\overline{BC}=2$

now for $\overline{CN}=\overline{SB}$
now, there is an equation to solve here, figure out what x equals
$4x-1 = 2x+7$    add one to both sides
$4x = 2x+8$     remove 2x from both sides
$2x = 8$       divide by 2 on both sides
$x = 4$      Answer for x

now that we know x, we can plug it in to find $\overline{CN}$ and $\overline{SB}$
$\overline{CN} = 4(4)-1$     $4 \times 4$ first
$16-1$    remove 1
$\overline{CN} = 15$

so your answer for $\overline{CN}$ is 15

now plug in 4 for x in the $\overline{SB}$ equation
$\overline{SB} = 2(4)+7$      $2 \times 4$ first
$8+7$      add together
$\overline{SB} = 15$ 
so your answer for $\overline{SB}$ is 15 (like it should be

there is your help for question #3

Extrinix · Answer

If you need any more assistance then this, feel free to dm me.

Shasha14 · Answer

Thanks

Extrinix · Answer

You're welcome.

Madiron · Answer

damn Ext,you are smart

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