Question

Can someone please help with this questions?

Answer 1

Answer:

5a. ΔGKM ~ ΔSPM by SAS

b. ΔABC is not similar to ΔDEF

6. The missing side is 2$\sqrt{11}$

Step-by-step explanation:

5a. Yes, the triangles are similar.

<KMG ≅ <PMS (vertically opposite angles)

      ΔGKM ~ ΔSPM by SAS

Ratio: GM:SM OR KM:PM

             3:6    OR  2:4

             1:2     OR  1:2

Ratio: 1:2

b. No, the triangles are not similar

   ΔABC is not similar to ΔDEF

Ratio: AC:DF OR AB:DE

         4:6       OR  2:4.5

         1:1.5      ≠     1:2.25

   Ratio: not similar

6. let the missing side of the triangle be represented by x. Since the triangle is a right angled triangle, then applying the Pythagoras theorem we have;

$/hyp/^{2}$ = $/adj 1/^{2}$ + $/adj2/^{2}$

$/12/^{2}$ = $x^{2}$ + $/10/^{2}$

144 = $x^{2}$ + 100

$x^{2}$ = 144 - 100

   = 44

x = $\sqrt{44}$

  = $\sqrt{4 *11}$

  = 2$\sqrt{11}$

x = 2$\sqrt{11}$

The missing side is 2$\sqrt{11}$.