Answer:
5a. ΔGKM ~ ΔSPM by SAS
b. ΔABC is not similar to ΔDEF
6. The missing side is 2[tex]\sqrt{11}[/tex]
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;
[tex]/hyp/^{2}[/tex] = [tex]/adj 1/^{2}[/tex] + [tex]/adj2/^{2}[/tex]
[tex]/12/^{2}[/tex] = [tex]x^{2}[/tex] + [tex]/10/^{2}[/tex]
144 = [tex]x^{2}[/tex] + 100
[tex]x^{2}[/tex] = 144 - 100
= 44
x = [tex]\sqrt{44}[/tex]
= [tex]\sqrt{4 *11}[/tex]
= 2[tex]\sqrt{11}[/tex]
x = 2[tex]\sqrt{11}[/tex]
The missing side is 2[tex]\sqrt{11}[/tex].
