5.5 Triangle Inequalities

List the three sides from shortest to longest of triangle pqr when given certain angle measurement

Find variable by using triangle sum theorem Then using side-angle inequality postulate, order the sides Be careful with you numbering

For listing the sides in order from smallest to largest when given the angles

Do the same thing as above, but now with sides Order the angles still one being the smallest Fill in middle Use side-angle inequality postulate Order of letter doesn't matter Angle to side Draw the image if not given Be careful

When arranging the unknown measures with two triangles that share a side

Draw the triangles separately Use congruency signs Order each triangles signs and then combine Put the biggest triangles sides first if there is a bigger triangle For this case

Explain why the measurement of angle one is greater than the measurement of angle two

Hard Ea theorem Previous knowledge + equations are key AIA Like if the ea is one and two plus three equal one because of the ea theorem, then one must be greater than two if it helps add up to it Or using substitution

Learned two

Postulates

For arranging the unknown measures from greatest to least

Pretty simple Find missing angle (if missing) using triangle sum theorem Use side-angle postulate to know that smallest side opposite is smallest angle and same with largest side Draw lines Show work Be careful

Triangle Inequality Postulate

The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Can write it out to check the sides Third side is greater the difference and less than the sum

Use previous knowledge

+ two new postulates sin this lesson Triangle sum theorem

List the angles of each teiangle in order from smallest to largest

Be careful it says smallest to largest Side-angle inequality postulate Biggest+ smallest find and then dill in the middle Biggest side opposite of biggest measure Draw line Side to angle here Order the sides one being the smallest and three being the largest Then start with one and see which angle is opposite, that is the smallest angle Then do the same with three And fill in two (the middle #)

Side-angle inequality postulate

In a triangle, the longest sides is opposite the angle with the biggest measure, and the shortest side is opposite the angle with the smallest measure. Opposite the smallest measure Or if given biggest angle, sign opposite of it is the longest side Vise verse Angle opposite of side Shortest then opposite smallest measure

Side-angle inequality postulate works for

Shortest and smallest side Use it either given largest/smallest side opposite is biggest/smaller measure Or biggest/smallest measure and the largest/smallest side is opposite it

Given angles then order sides or

Sides then order angles Use previous knowledge + side-angle inequality postulate

Be careful to see if it say order them

Smallest to largest or largest to smallest On note we did largest to smallest, but on hw we did smallest to largest

A student draw a triangle with a perimeter of 26. He says rhe longest side measures 18c,. How do you know that this is incorrect?

The two sides have to be greater than eighteen and the littlest number that is greater than eighteen is nineteen. 18 + 19=37, which is too great of a perimeter Greatest could be 17 I think Be careful

Find out the third angle using the

Triangle sum theorem

Determine which side is shortest in the diagram

Triangle sum theorem Draw triangles separately Find the shortest side in both triangles One of them will be the shared side So one triangle will have both the smallest of the other and its smallest Since you know its smallest is the smallest thats how you determine which side is the smallest

Can a triangle have the sides with the given lengths + explain

What you do is you use the triangle inequality pos You say x side plus x side must be greater than the third side Then you do this with all side combinations Will have three equations in total Then you check if the equations are all true If one of them isn't then the answer to the question is no Sum same as third side would then just be a straight line and sum too little, the triangle side would be too short Don't care about difference

Too short of a third side

Wouldn't connect and the sum the same as the third side would just be a line

The lengths of the two sides of a triangle are given. Describe the possible lengths of the third side

X is greater than the difference and less then the sum of the two numbers Both signs face open to the right Be careful adding/subtracting Third side of a triangle have to be greater then the difference of the two other sides Cause of folding the sides down