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# Triangles

### Point of Minimal Distance : Equilateral Triangle

Using GEOMETRY ONLY, for an equilateral triangular region, for which points is the sum of the distances to the sides of the triangle minimal? Please show me and do not point to a web site.

### Deriving Angle Functions

Given the degrees to two angles of a triangle. A =65º, b = 40º Derive the degrees in the angle c.

### Triangle angles

Given triangle ABC with no angle >120 degrees, find and construct the point P for which PA + PB + PC is a minimum. What is this point called? What would be the case for a triangle with an angle of 120 degrees or more?

### Symbolic Logic : Symbolic Notation

Determine whether or not the argument below is valid. Transcribe it into symbolic notation and if it is valid, provide a derivation of the conclusion from the premises using only primitive rules of inference. The area of a triangle is the area of a three sided figure. Since triangles are three sided.

### Metric space and triangle inequality.

Prove that in a metric space, if C lies between A and B and O is any other point, then OC<=OA + OB. (Hint make 3 applications of the triangle inequality) Triangle inequality: For triangle ABC AB+BC=>AC

### Area of Triangles: Moving Partitions

Please see the attached file for the fully formatted problems.

### Two triangles: The lengths of the sides opposite the angles.

In this question ABC and PQR are two triangles, and the lengths of the sides opposite the angles A,B,C P, Q, R are a,b,c,p,q,r, respectively. Choose the THREE false statements. Options. A. If angle A= angle Q and angle B= angle P. then it must follow that c b --- = -- r p B. I

### Find the angle in a triangle

Suppose that the triangle ABC has three edges a=BC=4sqrt(3) , b=AC=4 and c=AB=4. Find angle ABC and BAC.

### The Radius of the Circumscribed circle for a triangle

The circumscribed circle is the circle passing through the three vertices of a triangle ABC. Assume the following results from geometry. The perpendicular bisectors of the sides of a triangle meet in a point O that is the center of the circumscribed circle. a) According to a theorem from geometry, the measure of the angle

### Perimeter and area of triangle

In triangle ABC, the lengths of line AB and line BC equal 13 centimeters. If the perimeter of triangle ABC is 36 centimeters, what is the area in square centimeters of triangle ABC?

### Geometry: A 1 acre area field in the shape of a right triangle has a post at the midpoint of each side. What is thw total area the two sheep have to themselves?

A 1 acre area field in the shape of a right triangle has a post at the midpoint of each side. A sheep is tethered to each side posts and a goat to the post in the hypotenuse. The ropes are just long enough to let each animal reach the two adjacent vertices. What is thw total area the two sheep have to themselves? i.e. the area t

### Total area of a triangle

A 1 acre field in the shape of a right triangle has a post at the midpoint of each side. A sheep is tethered to each of the side of the post on the hypotenuse. The ropes are just long enough to let each animal reach the two adjacent vertices. What is the total area the two sheep have to themselves?

### Solving for an unknown side in a right angle triangle.

A triangle with a 90 degree angle has sides of 39, 15, b. Solve for b.

### Constructing a right angled triangle.

Construct a right angled triangle such that the altitude to the hypotenuse and the median to the hypotenuse have lengths r and s respectively.

### Geometric proof

Prove that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.

### Right triangles

How do I find the third angle in a right angle triangle if I know one of the angle's is 65 deg?

### Solving for x using multiple triangles. Question in JPG format.

Solve for x. Diagram in attachment below.

### Determining the Congruence of Triangles

Segment PA is congruent to plane m Points A,B,C,and D lie in plane m Segment AB is congruent to segment AD Is triangle PAB congruent to triangle PAD?

### Sum of interior angles

Find the sum of the interior angle of:pentagon,15-gon,and 18-gon.