From the inequalities in the triangles shown, Jarold concluded that ∠OHM > ∠EHM. Which theorem on inequalities in triangle justifies his answer?

• Triangle Inequality Theorem 3 (S1 + S2 > S3)

• Hinge Theorem

• Triangle Inequality Theorem 1 (Ss →Aa)  

• Converse of Hinge Theorem

Tags

CCSS.HSG.CO.C.9

Chris forms triangles by bending a 16-inch wire. Which of the following sets of wire lengths

               successfully form a triangle?           

I. 4 in, 5 in, 6 in                     III. 4 in, 5 in, 7 in  

 II. 4 in, 4 in, 8 in                    IV. 3 in, 4 in, 9 in

     

• I, II   

• III, IV  

• II, IV  

• I, III

Tags

CCSS.7.G.A.2

Notice that m∠5 > m∠3 and m∠5  > m∠1. Which theorem justifies these observations?

   

• Triangle Inequality Theorem 1 (Ss →Aa)    

• Triangle Inequality Theorem 2 (Aa → Ss)     

• Triangle Inequality Theorem 3 (S1 + S2 > S3 )

• Exterior Angle Inequality Theorem

Tags

CCSS.8.G.A.5

Which of the following angles is an exterior angle of  ΔRPY?       

• ∠2  

• ∠3

• ∠4

• ∠7

Tags

CCSS.8.G.A.5

Which of the following is not an inequality theorem for one triangle?

• Triangle Inequality Theorem 1 (Ss →Aa)

• Exterior Angle Inequality Theorem

• Triangle Inequality Theorem 3 (S1 + S2 > S3)

• Hinge Theorem

From the inequalities in the triangles shown, a conclusion can be reached using the converse of hinge theorem. Which of the following is the last statement?

• HM ≅ HM

• m∠OHM > m∠EHM

• HO ≅ HE

• m∠EHM > m∠OHM

Tags

CCSS.HSG.CO.C.9

Which side of ΔGOD is the shortest?

• 𝐺𝑂

• 𝐷𝑂

• 𝐷𝐺

• 𝐺𝐷

Tags

CCSS.HSG.CO.C.10

Each of Xylie, Marie, Angelo and Chris was given an 18-inch piece of stick. They were instructed to create a triangle. Each cut the stick in their own chosen lengths as follows: Xylie - 6 in, 6 in, 6 in; Marie - 4 in, 5 in, 9 in; Angelo - 7 in, 5 in, 6 in; and Chris - 3 in, 7 in, 5 in. Who among them was not

able to make a triangle?

• Xylie

• Marie

• Angelo

• Chris

Tags

CCSS.7.G.A.2

The measure of an exterior angle of a triangle is always ____________.

• greater than its adjacent interior angle.

• greater than either remote interior angle.

• less than its adjacent interior angle.

• less than either remote interior angle.

Tags

CCSS.8.G.A.5

Which side of the triangle is the shortest?

• (DV)

• (VE)

• (ED)

• (VD)

Tags

CCSS.HSG.CO.C.10