Triangles

Name Computer Number

Construct Triangle ABC.

Measure , , and . The sum of the angles is .

Measure the sides of the Triangle. AB , BC , and AC .

Classify the Triangle.

(Acute, Obutse, Right, Equiangular, Equilateral, Scalene, Isosceles)

My triangle is .

Make the triangle a right, scalene triangle. (Let = 90 degrees)

AB = BC = AC = = = =

What can you conclude about and ?

AC is called the . BC and AB are called the of the triangle.

Make the triangle an obtuse, isosceles triangle. (Let be obtuse, and AB = AC)

AB = BC = AC = = = =

What can you conclude about and ?

is called the angle. and are called the angles.

Make the triangle equilateral.

AB = BC = AC = = = =

What can you conclude about ,, and ?

If a triangle is equilateral, then it is also .

Construction

Construct horizontal segment AB.

Construct a point on segment AB (move point closer to point A), label as F.

From point F, construct segment FC with a positive slope.

Construct a point on segment FC (move point closer to point C), label as D.

Construct segment DE through point B so that DB + BE = DE.

(Your construction should look like the one shown below.)

Name the triangle. = = =

Name the three exterior angles and their two remote interior angles of the triangle and give their measurement.

 exterior angle two remote interior angles , , ,

What can you conclude about the relationship between each exterior angle of a triangle and its two remote interior angles?

What can you conclude about the relationship between each interior angle of the triangle and its corresponding exterior angle and why?

Construct triangle ABC. Let AB = 5, BC = 8, and AC = 5.

= = =

Which angles are congruent?

Complete the following statements using the "Isosceles Triangle Theorem" (ITT)

If two sides of a triangle are congruent, then .

If two angles of a triangle are congruent, then .

Problem (show all work)

In isosceles triangle RST, is the vertex angle. If = 7x - 17 and = 3x + 35, and = 2x + 6, find the measure of each angle of the triangle.