01_8TH GRADE - MATH 4Q [APPLYING THEOREMS ON TRIANGLE INEQUALIT]

Carlos concluded that the longest side in 𝛥𝑀𝐴𝑃 is 𝐴𝑃̅̅̅̅ after finding that the angle opposite to 𝐴𝑃̅̅̅̅ is the largest angle. What theorem did Carlos use to make such conclusion?

• Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)
• Triangle Inequality Theorem 2 (𝐴𝑎 → 𝑆𝑠)
• Hinge Theorem or SAS Triangle Inequality Theorem
• Converse of Hinge Theorem or SSS Triangle Inequality Theorem

Liza, Kathryn, and Nadine were each given a 21-inch piece of stick. They were instructed to create a triangle. Each stick was cut in their own chosen lengths as follows: Liza - 6 𝑖𝑛, 7 𝑖𝑛, 8 𝑖𝑛; Kathryn - 4 𝑖𝑛, 6 𝑖𝑛, 11 𝑖𝑛; and Nadine - 3 𝑖𝑛, 5 𝑖𝑛, 13 𝑖𝑛. Who among them was able to make a triangle?

• Liza
• Nadine
• Kathryn
• All of them

Which of the following lengths in cm are possible measures of the sides of a triangle?

• 1,2,3
• 4,5,10
• 5,6,7
• 5,9,15

Which of the following theorems will support your answer in number 8?

• Exterior Angle Inequality Theorem
• Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)
• Triangle Inequality Theorem 3 (𝑆1 + 𝑆2 > 𝑆3)
• Converse of Hinge Theorem or SSS Triangle Inequality Theorem

Which is always true about the measure of an exterior angle of a triangle?

• A. It is less than the measure of its adjacent interior angle.
• B. It is less than the measure of either remote interior angle.
• C. It is greater than the measure of its adjacent interior angle.
• D. It is greater than the measure of either remote interior angle.

Which of the following numbers of the same unit could represent the side lengths of a triangle?

• 1,2,5
• 2,4,5
• 3,6,10
• 4,5,11

What theorem supports this statement, “In an obtuse triangle, the longest side is opposite the obtuse angle.”

• Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)
• Triangle Inequality Theorem 2 (𝐴𝑎 → 𝑆𝑠)
• Hinge Theorem or SAS Triangle Inequality Theorem
• Converse of Hinge Theorem or SSS Triangle Inequality Theorem

What is the largest angle?

• ∠E

• ∠N

• ∠P

• Cannot be Determined

What is the smallest angle?

• ∠E

• ∠N

• ∠P

• Cannot be Determined

Which side of ∆𝑇𝐼𝑃 is the longest?

• Cannot be determined