Definitions
The sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.
TRIANGLE INEQUALITY THEOREM
Could a triangle have side length as 6cm, 7cm and 5cm?
6 + 7 > 5 ⇒ 13 > 5 ⇒ True
7 + 5 > 6 ⇒ 12 > 6 ⇒ True
6 + 5 > 7 ⇒ 11 > 7 ⇒ True
CAN FORM A TRIANGLE
Which is the largest angle?
A. ∠𝐷
B. ∠𝑂
C. ∠𝑃
D. Cannot be determined
B. ∠𝑂
. Given below is ∆𝐴𝑅𝑇. List the sides from the longest to the shortest.
A. 𝐴𝑇̅̅̅̅, 𝐴𝑅̅̅̅̅, 𝑅𝑇̅̅̅̅
B. 𝐴𝑅̅̅̅̅, 𝑇𝑅̅̅̅̅, 𝑇𝐴̅̅̅̅
C. 𝑅𝑇̅̅̅̅, 𝑅𝐴̅̅̅̅, 𝑇𝐴̅̅̅̅
D. 𝑇𝐴̅̅̅̅, 𝑇𝑅̅̅̅̅, 𝐴𝑅̅̅̅̅
A. 𝐴𝑇̅̅̅̅, 𝐴𝑅̅̅̅̅, 𝑅𝑇̅̅̅̅
The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle
EXTERIOR ANGLE INEQUALITY THEOREM
If 4cm, 8cm and 2cm are the measures of three lines segment. Can it be used to draw a triangle?
4 + 8 > 2 ⇒ 12 > 2 ⇒ True
8 + 2 > 4 ⇒ 10 > 4 ⇒ True
4 + 2 > 8 ⇒ 6 > 8 ⇒ False
CANNOT FORM A TRIANGLE
What is the measure of ∠Y?
90°
If two angles of a triangle are not congruent, then the larger side is opposite the larger angle
ANGLE-SIDE INEQUALITY THEOREM
TRUE OR FLASE
Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
True
Which angle has the greatest measure?
∠B
If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is greater than the included angle of the second, then the third side of the first triangle is longer than the third side of the second.
HINGE THEOREM OR SAS INEQUALITY
Peter has three measurements with him: 6 cm, 10 cm, and 17 cm. Will he be able to form a triangle with these three measurements?
6 + 10 > 17
⇒ 16 > 17 (false, 17 is not less than 16)
6 + 17 > 10
⇒ 23 > 10 (this is true)
10 + 17 > 6
⇒27 > 6 (this is true)
What is the largest Angle?
∠E
If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second
CONVERSE OF THE HINGE THEOREM OR SSS INEQUALITY
Which of the following is NOT true about the Triangle Inequality Theorem?
1. AB + BC > AC
2. AB + AC < BC
3. BC + AC > AB
2. AB + AC < BC
Which is greater?
m∠1
Arrange the angles of ∆𝐴𝐵𝐶 from greatest to least measure given the lengths of its sides.
1. |𝐴𝐵| = 5 𝑐𝑚, |𝐵𝐶| = 10 𝑐𝑚, |𝐴𝐶| = 12 𝑐𝑚
AC,BC,AB