b. This is an equilateral,or equiangulartriangle.It is also acute.
c. This is a scalenetriangle,but it is also a right triangle.
Whilethereare differenttypesof triangles,all triangleshaveone thingin common:the sum of the interior
anglesin a triangleis always 180 o. You can see why this true if you rememberthat a straightline formsa
“straightangle,”whichmeasures 180 o. Nowconsiderthe diagrambelow, whichshowsthe triangleABC,
and a line drawnthroughvertexB, parallelto side AC. Belowthe figureis a proofof the triangleanglesum.
- If we considersidesAB and CB as transversalsbetweenthe parallellines,then we can see that angle
A and angle1 are alternateinteriorangles. - Similarly, angleC and angle2 are alternateinteriorangles.
- ThereforeangleA and angle1 are congruent,and angleC and angle2 are congruent.
- Now note that angles1, 2, and B form a straightline. Thereforethe sum of the threeanglesis 180o.
- We can completethe proofusingsubstitution: