Unit 4 Toolbox

Recall the 4.1 Triangle Sum Conjecture Investigation to fill in the blanks for #1, #2 and #3.

https://www.geogebra.org/m/vgraxtqj

Please write degree units using the degree symbol on the keyboard provided.

1

Triangle Sum Conjecture
The sum of the measures of the interior angles in every triangle is ______________.

1

What is the sum of the exterior angles in a triangle?

1

Triangle Exterior Angle Conjecture
The measure of an exterior angle of a triangle is _________________________to the sum of the measures of the two remote, interior angles.

Recall from the Unit 1 Toolbox the classifications of triangles by side length. Fill in the blanks for questions #4, #5, #6 and #7 using this information.

1

Definition of a Scalene Triangle
A scalene triangle is a triangle with _________________________________________.

1

Definition of an Isosceles Triangle (isos means equal)
An isosceles triangle is a triangle with ________________________________________.

1

Defintion of an Equilateral Triangle ("equi" means equal and lateral means sides)
An equilateral triangle is a triangle with ________________________________________.

1

An equilateral triangle is an isosceles triangle.

Tačno

Netačno

Recall the GeoGebra 4.2 Properties of Isosceles Triangles. Use this information to fill in the blank for question #8.

https://youtu.be/bekhfS1BMk8

1

Isosceles Triangle Conjecture
If a triangle is isosceles, then the base angles are _________________________.

The Converse of the Isosceles Triangle Conjecture is also true. It states that if a triangle has two congruent angles, then the sides across from those angles are also congruent. Use this information to mark two sides congruent on the triangle for #9.

1

Equilateral/Equiangular Triangle Conjecture
Since equilateral triangles are isosceles triangles, they have multiple pairs of base angles. Therefore, equilateral triangles are also equiangular. Mark this triangle with three equal sides and three equal angles.

Recall the GeoGebra investigation 4.3 Triangle Inequalities. Use your observations to fill in the blanks for #10, #11 and #12.

https://www.geogebra.org/m/dpnbtrtr

1

Triangle Inequality Conjecture
The sum of the lengths of any two sides of a triangle is _______________________than the length of the third side.

1

Using the Triangle Inquality Conjecture, we can determine that a side of a triangle must be greater than the difference of the other two sides and less than the sum of the other two sides.
Which of these side lengths are possible if two sides of the triangle are 6 and 7 cm?

1

Unequal Sides and Angles Conjecture (please place a comma between your answers)
The smallest angle is directly across from the _side length.
The largest angle is directly across from the __side length.

Recall the GeoGebra activity https://www.geogebra.org/m/aedf7yzx for question #14.

1

Which of these congruence conjectures ALWAYS result in congruent triangles?

1

CPCTC
If two triangles are congruent, then the Corresponding Parts of those Congruent Triangles are Congruent. Mark the congruent parts of these congruent triangles. You should mark three pairs of angles and three pairs of sides.

Unit 4 Toolbox

Triangle Sum ConjectureThe sum of the measures of the interior angles in every triangle is ______________.

What is the sum of the exterior angles in a triangle?

Triangle Exterior Angle ConjectureThe measure of an exterior angle of a triangle is _________________________to the sum of the measures of the two remote, interior angles.

Definition of a Scalene TriangleA scalene triangle is a triangle with _________________________________________.

Definition of an Isosceles Triangle (isos means equal)An isosceles triangle is a triangle with ________________________________________.

Defintion of an Equilateral Triangle ("equi" means equal and lateral means sides)An equilateral triangle is a triangle with ________________________________________.

An equilateral triangle is an isosceles triangle.

Isosceles Triangle ConjectureIf a triangle is isosceles, then the base angles are _________________________.

Equilateral/Equiangular Triangle ConjectureSince equilateral triangles are isosceles triangles, they have multiple pairs of base angles. Therefore, equilateral triangles are also equiangular. Mark this triangle with three equal sides and three equal angles.

Triangle Inequality ConjectureThe sum of the lengths of any two sides of a triangle is _______________________than the length of the third side.

Using the Triangle Inquality Conjecture, we can determine that a side of a triangle must be greater than the difference of the other two sides and less than the sum of the other two sides. Which of these side lengths are possible if two sides of the triangle are 6 and 7 cm?

Unequal Sides and Angles Conjecture (please place a comma between your answers)The smallest angle is directly across from the ___________________side length.The largest angle is directly across from the ____________________side length.

Which of these congruence conjectures ALWAYS result in congruent triangles?

CPCTCIf two triangles are congruent, then the Corresponding Parts of those Congruent Triangles are Congruent. Mark the congruent parts of these congruent triangles. You should mark three pairs of angles and three pairs of sides.

Triangle Sum ConjectureThe sum of the measures of the interior angles in every triangle is ______________.

What is the sum of the exterior angles in a triangle?

Triangle Exterior Angle ConjectureThe measure of an exterior angle of a triangle is _________________________to the sum of the measures of the two remote, interior angles.

Definition of a Scalene TriangleA scalene triangle is a triangle with _________________________________________.

Definition of an Isosceles Triangle (isos means equal)An isosceles triangle is a triangle with ________________________________________.

Defintion of an Equilateral Triangle ("equi" means equal and lateral means sides)An equilateral triangle is a triangle with ________________________________________.

An equilateral triangle is an isosceles triangle.

Isosceles Triangle ConjectureIf a triangle is isosceles, then the base angles are _________________________.

Equilateral/Equiangular Triangle ConjectureSince equilateral triangles are isosceles triangles, they have multiple pairs of base angles. Therefore, equilateral triangles are also equiangular. Mark this triangle with three equal sides and three equal angles.

Triangle Inequality ConjectureThe sum of the lengths of any two sides of a triangle is _______________________than the length of the third side.

Using the Triangle Inquality Conjecture, we can determine that a side of a triangle must be greater than the difference of the other two sides and less than the sum of the other two sides. Which of these side lengths are possible if two sides of the triangle are 6 and 7 cm?

Unequal Sides and Angles Conjecture (please place a comma between your answers)The smallest angle is directly across from the ___________________side length.The largest angle is directly across from the ____________________side length.

Which of these congruence conjectures ALWAYS result in congruent triangles?

CPCTCIf two triangles are congruent, then the Corresponding Parts of those Congruent Triangles are Congruent. Mark the congruent parts of these congruent triangles. You should mark three pairs of angles and three pairs of sides.

Triangle Sum Conjecture
The sum of the measures of the interior angles in every triangle is ______________.

Triangle Exterior Angle Conjecture
The measure of an exterior angle of a triangle is _________________________to the sum of the measures of the two remote, interior angles.

Definition of a Scalene Triangle
A scalene triangle is a triangle with _________________________________________.

Definition of an Isosceles Triangle (isos means equal)
An isosceles triangle is a triangle with ________________________________________.

Defintion of an Equilateral Triangle ("equi" means equal and lateral means sides)
An equilateral triangle is a triangle with ________________________________________.

Isosceles Triangle Conjecture
If a triangle is isosceles, then the base angles are _________________________.

Equilateral/Equiangular Triangle Conjecture
Since equilateral triangles are isosceles triangles, they have multiple pairs of base angles. Therefore, equilateral triangles are also equiangular. Mark this triangle with three equal sides and three equal angles.

Triangle Inequality Conjecture
The sum of the lengths of any two sides of a triangle is _______________________than the length of the third side.

Using the Triangle Inquality Conjecture, we can determine that a side of a triangle must be greater than the difference of the other two sides and less than the sum of the other two sides.
Which of these side lengths are possible if two sides of the triangle are 6 and 7 cm?

Unequal Sides and Angles Conjecture (please place a comma between your answers)
The smallest angle is directly across from the _side length.
The largest angle is directly across from the __side length.

CPCTC
If two triangles are congruent, then the Corresponding Parts of those Congruent Triangles are Congruent. Mark the congruent parts of these congruent triangles. You should mark three pairs of angles and three pairs of sides.

Triangle Sum Conjecture
The sum of the measures of the interior angles in every triangle is ______________.

Triangle Exterior Angle Conjecture
The measure of an exterior angle of a triangle is _________________________to the sum of the measures of the two remote, interior angles.

Definition of a Scalene Triangle
A scalene triangle is a triangle with _________________________________________.

Definition of an Isosceles Triangle (isos means equal)
An isosceles triangle is a triangle with ________________________________________.

Defintion of an Equilateral Triangle ("equi" means equal and lateral means sides)
An equilateral triangle is a triangle with ________________________________________.

Isosceles Triangle Conjecture
If a triangle is isosceles, then the base angles are _________________________.

Equilateral/Equiangular Triangle Conjecture
Since equilateral triangles are isosceles triangles, they have multiple pairs of base angles. Therefore, equilateral triangles are also equiangular. Mark this triangle with three equal sides and three equal angles.

Triangle Inequality Conjecture
The sum of the lengths of any two sides of a triangle is _______________________than the length of the third side.

Using the Triangle Inquality Conjecture, we can determine that a side of a triangle must be greater than the difference of the other two sides and less than the sum of the other two sides.
Which of these side lengths are possible if two sides of the triangle are 6 and 7 cm?

Unequal Sides and Angles Conjecture (please place a comma between your answers)
The smallest angle is directly across from the _side length.
The largest angle is directly across from the __side length.

CPCTC
If two triangles are congruent, then the Corresponding Parts of those Congruent Triangles are Congruent. Mark the congruent parts of these congruent triangles. You should mark three pairs of angles and three pairs of sides.