Theorems
Triangle Sum Theorem
What is the sum of all three angles in a triangle equal 180 degrees?
In △OMN, ∠O = 42° and ∠N = 117°. What does ∠M equal?
What is 21°?
Means the same.
What is congruent?
Draw a Right Triangle.
Has one 90 degree angle
∠
What is angle?
The sum of the two smaller sides must be greater than the third side to create a triangle.
What is the Triangle Inequality Theorem?
{22, 41, 9} Give reasoning.
Not a triangle because 22+9=31 and 31<41
angles inside a triangle
What are interior angles?
Draw an acute equilateral triangle.
three equal side lengths (shown by tick marks) and three angles under 90 degrees
°
What is degrees?
Hinge Theorem
What is given two triangles with two sets of congruent sides, the larger included angle has the larger third side?
From teachers drawing, is ∠BAC >, <, or = to ∠EDC
What is ∠BAC?
angles outside a triangle
What are exterior angles?
Draw an obtuse scalene triangle.
One angle above 90 degrees and all sides are different lengths (shown by tick marks)
≅
What is congruent?
AB ≅ AB
What is the Reflexive Property?
What are the congruency statements? Refer to teachers drawing. (sides and angles)
FG ≅ FG
FC ≅ FI
∠C≅∠I
∠FGI≅∠FGC
The angles opposite each other when two lines cross. Always equal.
What are vertical angles?
Draw an isosceles acute triangle.
two congruent sides (shown by tick marks) and all angles under 90 degrees.
∥
What is parallel?
Exterior Angle Theorem
What is the sum of the two interior adjacent angles equal the exterior angle?
From teachers drawing, how do you find ∠OJK.
- Use exterior angle theorem to find ∠JOK.
-Subtract ∠JOH=140 from 180 and get ∠JOK=40.
-Add ∠JOK=40 and ∠JKO=30, to get 70 degrees.
-Subtract 70 from 180 using triangle sum theorem.
-Solution is ∠OJK=110.
Two straight lines that are always the same distance apart and never touch.
What are parallel lines?
Draw two acute scalene triangles that have vertical angles.
two triangles with angles under 90 degrees, all unequal sides (shown with tick marks), two of the angles are opposite each other and equal each other.
⊥
What is perpendicular?