Triangle Inequalities

Which side length could NOT form a triangle?

• 5m, 6m, 8m

• 10m, 10m, 2m

• 19m, 34m, 15m

• 3m, 16m, 14m

Two sides of a triangle measure 10 feet and 14 feet. Which inequality shows the possible lengths for the third side, x?

• $10\le x\le14$

• $4\le x\le24$

• $10<x<14$

• $4<x<24$

Two sides of a triangle measure 27 inches and 32 inches. Which could represent the length of the third side?

• 5 in

• 7 in

• 59 in

• 62 in

Which inequality correctly shows the relationship of the angles in  $\Delta JKL$  ?

•  $m\angle K\ <\ m\angle L\ <\ m\angle J$  

•  $m\angle J\ <m\angle L\ <m\angle K$  

•  $m\angle L\ <\ m\angle J\ <\ m\angle K$  

•  $m\angle K\ <\ m\angle J\ <\ m\angle L$  

Which inequality correctly shows the relationship of the sides of  $\Delta ABC$  ?

•  $AC>BC>AB$  

•  $AC<BC<AB$  

•  $AB>BC>AC$  

•  $BC<AB<AC$  

Which inequality correctly shows the relationship of the sides shown in the diagram?

• $\overline{ZY}\ >\ \overline{WX}$

• $\overline{ZY}\ <\ \overline{XY}$

• $\overline{XY}\ =\overline{ZY}$

• $\overline{XY}<\overline{ZY}$

In  $\Delta PQR,$  $m\angle P=5x+7,$   $m\angle Q=3x-11,$  and  $m\angle R=7x-26.$   Which inequality shows the relationship of the sides?

•  $PR>PQ>QR$  

•  $PR<QR<PQ$  

•  $QR>PQ>PR$  

•  $PQ<QR<PR$  

In  $\Delta CDE$ ,  $CD=2x+1$ ,  $DE=3x-4$ , and  $CE=x+1$ . If the perimeter of the triangle is 52 meters, which inequality shows the relationship of the angles?  

•  $m\angle D<m\angle E<m\angle C$  

•  $m\angle D<m\angle C<m\angle E$  

•  $m\angle D>m\angle E>m\angle C$  

•  $m\angle D>m\angle C>m\angle E$  

In $\Delta MNP$ ,  $MN=5x+19$ ,  $NP=4x-1$ , and  $MP=10x-7$ . Which inequality shows the possible values of x?   

•  $9<x<31$  

•  $3<x<25$  

•  $3<x<13$  

•  $11<x<25$  

In $\Delta RST$ ,  $RS=x+15$ ,  $ST=8x-26$ , and  $RT=3x+1$ . Which inequality shows the possible values of x?    

•  $2<x<10.5$  

•  $2<x<4$  

•  $4<x<10.5$  

•  $4<x<26$