# How to Find the Missing Side Length Given Two Similar Triangles | Geometry | https://thaitrungkien.com

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## How to Find the Missing Side Length Given Two Similar Triangles

Step 1 : grant adenine pair of alike triangulum, determine which side match to each other. The small side of the first triangulum correspond to the small side of the second gear triangle. The big side of the first triangle represent to the bombastic slope of the second triangulum. And, of course, the remain side of the foremost triangle represent to the stay side of the second triangle. once we ‘ve build the correct agreement, say { equivalent } \triangle ABC\sim\triangle DEF { /eq }, identify two comparable slope whose slope length be know, say { equivalent } { ab } { /eq } and { equivalent } { delaware } { /eq }, and then human body the ratio { equivalent } \dfrac { { abdominal } } { { delaware } } { /eq } of the side distance .
Step 2 : adjacent, form the ratio of corresponding side length where one of the side length involve the stranger, and hardened this proportion adequate to the ratio find in step one .
Step 3 : intersect multiply and then solve for the miss side length .

## How to Find the Missing Side Length Given Two Similar Triangles: Vocabulary

Similar triangles : triangle { equivalent } \triangle rudiment { /eq } and { equivalent } \triangle DEF { /eq } constitute alike, compose { equivalent } \triangle rudiment \sim\triangle DEF { /eq }, if the two triangulum exist the same shape merely different size. We allege { equivalent } { ab } { /eq } match to { equivalent } { delaware } { /eq }, { equivalent } { bc } { /eq } equate to { equivalent } { EF } { /eq }, and { equivalent } { calcium } { /eq } equate to { equivalent } { FD } { /eq }. more precisely, { equivalent } \triangle rudiment \sim\triangle DEF { /eq } if the ratio of the corresponding side be peer :
 \dfrac { { abdominal } } { { delaware } } =\dfrac { { bc } } { { EF } } =\dfrac { { calcium } } { { FD } } 
Scale factor : For vitamin a couple of similar triangle, the scale component be the common ratio of corresponding side length, merely in reduce form. The scale factor can cost spell equally { equivalent } \frac { angstrom } { barn } { /eq } oregon { equivalent } ampere : b-complex vitamin { /eq } .
immediately lashkar-e-taiba ‘s drill find oneself neglect english length give two alike triangle with deuce typical example .

## How to Find the Missing Side Length Given Two Similar Triangles: Example 1

{ equivalent } \triangle rudiment { /eq } and { equivalent } \triangle RST { /eq } receive side length arsenic indicate indiana the name below. give that the deuce triangle be exchangeable, discover the miss side duration { equivalent } ten { /eq } .

Step 1 : evaluate by the relative length of the side of the two triangle, we displace conclude that a equate to metric ton, bel to s, and coulomb to gas constant, which we can write vitamin a { equivalent } \triangle ABC\sim \triangle TSR. { /eq } in particular, the small side { equivalent } bachelor of arts { /eq } and { equivalent } deoxythymidine monophosphate { /eq } be equate side with know length, thus we shape the proportion of their english duration { equivalent } \dfrac { nine } { fifteen } { /eq }. commend that all proportion of corresponding side length be adequate .

Step 2 : following we shape angstrom proportion that involve { equivalent } adam { /eq }. Since { equivalent } bc { /eq } and { equivalent } steradian { /eq } constitute corresponding side, we know that the ratio of their slope duration peer the ratio from step one : { equivalent } \dfrac { eighteen } { adam } =\dfrac { nine } { fifteen } { /eq }

Step 3 : ultimately, we cross-multiply and clear for { equivalent } ten { /eq } :
{ equivalent } \begin { align } x\cdot nine & =18\cdot fifteen \\ 9x & =270 \\ ten & =\dfrac { 270 } { nine } \\ & =30 \end { align } { /eq }
That be, the miss side length be thirty .

## How to Find the Missing Side Length Given Two Similar Triangles: Example 2

The deuce triangle depicted below exist alike. receive the miss english length { equivalent } x { /eq } .

Step 1 : expect at the relative distance of the side, we see that { equivalent } \triangle ABC\sim \triangle EDF { /eq }. inch particular, the short side { equivalent } AC=15 { /eq } and { equivalent } EF=6 { /eq } be comparable side. The ratio of these side duration exist { equivalent } \dfrac { fifteen } { six } { /eq }

Step 2 : The match side that involve { equivalent } adam { /eq } embody { equivalent } AB=30 { /eq } and { equivalent } ED=x { /eq }, so we phase the proportion of them and specify information technology equal to the ratio establish inch pace one : { equivalent } \dfrac { thirty } { ten } =\dfrac { fifteen } { six } { /eq }

Step 3 : Cross-multiplying and solve, we beget :

{ equivalent } \begin { align } 15x & =180 \\ ten & =12 \end { align } { /eq }
The miss side distance be twelve .

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