Problem 1 Using the Side-Splitter Theorem

GRIDDED RESPONSE

What is the value of x in the diagram below?

P K K M = N L L M Side-Splitter Theorem x + 1 12 = x 9 Substitute . 9 x + 9 = 12 x Cross Products Property 9 = 3 x Subtract  9 x  from each side . 3 = x Divide each side by  3. table with 5 rows and 3 columns , row1 column 1 , fraction p k , over k m end fraction , column 2 equals . fraction n l , over l m end fraction , column 3 cap sideminuscap splittercap theorem , row2 column 1 , fraction x plus 1 , over 12 end fraction , column 2 equals , x over 9 , column 3 cap substitute . . , row3 column 1 , 9 x plus 9 , column 2 equals 12 x , column 3 cap crosscap productscap property , row4 column 1 , 9 , column 2 equals 3 x , column 3 cap subtract . 9 x . fromeachside . . , row5 column 1 , 3 , column 2 equals x , column 3 cap divideeachsideby . 3. , end table

Grid in the number 3.

✓ Got It?

1. 1. What is the value of a in the diagram below?

      

   2. Reasoning In △ X Y Z , white up pointing triangle x y z comma   R S ¯ r s bar  joins X Y ¯ x y bar  and Y Z ¯ y z bar  with R on X Y ¯ x y bar  and S on Y Z ¯ , y z bar , comma  and R S ¯ ‖ X Z ¯ . r s bar . double vertical bar , x z bar . .  If Y R R X = Y S S Z = 1 , fraction y r , over r x end fraction . equals . fraction y s , over s z end fraction . equals 1 comma  what must be true about RS? Justify your reasoning.