Prove:.
- Considerisoscelestriangle with , and ,.
Prove:.
Answers
All four pointsare the same.
The four pointsall lie insidethe triangle.
The four pointsall lie outsidethe triangle.
The orthocenterlies on the vertexof the right angleand the circumcenterlies on the midpointof the hy-
potenuse.
The orthocenter, the circumcenter, and the centroidare alwayscollinear.
a. The circumcenterand the orthocenterare the endpointsof the Eulersegment.b. The distancefrom the orthocenterto the centroidis twicethe distancefrom the centroidto the circumcenter.- Threeof the pointsare the midpointsof the triangle’s sides.Threeotherpointsare the pointswherethe
altitudesintersectthe oppositesidesof the triangle.The last threepointsare the midpointsof the segments
connectingthe orthocenterwith eachvertex. - The congruencecan be provenby showingthe congruenceof triangles and. This
can be doneby applyingpostulateAAS to the two triangles.