Geometry Answers

Show that if a and b are
(a) in the same direction then |a + b| = |a| + |b|,
(b) in the opposite direction then |a − b| = |a| + |b|.

Prove the following:
The sides of the orthic triangle meet the sidesof the given triangle in three collinear points.

show that cos2a+cos2B+cos2r=1

The base angles of some isosceles triangle are 80°. Point D is on segment AC and point E is on AB such that ∠DBC = 60 and ∠ECB 50 . Find the angle EDB.

Draw triangle xyz with vertices x(-3,2),Y(4,-2), and z(-3,-2) on the coordinate plane.Then find the area of the triangle in square units

Let P be a point inside triangle ABC such that
∠AP B − ∠ACB = ∠AP C − ∠ABC.
Let D, E be the incenters of triangles AP B, AP C, respectively. Show that
AP, BD, CE meet at a point.

Prove that in a right triangle, the bisector of the right angle halves the angle between the median and altitude drawn from the same vertex.

Triangle ABC is inscribed in a circle. A median AM is drawn so that it intersects
the circle at point D. It is known that AB=1 and BD=1. Find BC.

Which is different?












Question 2
Find “both” answers.

The answer to the question chosen is (answer)
units. The answer to the three questions not chosen is (answer)
square units.

How are rectangles and rhombus the same