Learning Activity 3: Direction: Find the measure of the unknown angles and
sides of the given parallelogram as shown in the figure below. Show your
Solution
S
M
T
E
A
L
Rectangle PSAL has a
diagonal mPA = 16
cm. Find:
1. MPM =
Rhombus SAMT with
MLSTM = 60°
Square FGH
Find
5 m4GH =
3. mz MTA =
mTSM =
(with Solution po)
sides of the given parallelogram as shown in the figure below. Show your
Solution
S
M
T
E
A
L
Rectangle PSAL has a
diagonal mPA = 16
cm. Find:
1. MPM =
Rhombus SAMT with
MLSTM = 60°
Square FGH
Find
5 m4GH =
3. mz MTA =
mTSM =
(with Solution po)
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Answers & Comments
Answer:
1. PM = 8
2. SL = 16
3. MTA = 30 degrees
4. TSM = 60 degrees
5. G J H = 60 degrees
Step-by-step explanation:
1.PA =16
M is the midpoint
Hence, PM = PA/2
PM = 16/2 = 8
2. PA = SL
Property of parallelogram
PA = 16
SL = 16
3. STM = 60 degrees
divided into half by a line creates angles ATM and ATS
MTA = STM/2
MTA = 60/2
MTA = 30 degrees
4. Angle E = 90
ATS = STM/2 = 60/2 = 30
all triangle's angles add up to 180
180 = 90 + 30 + TSM
180 - 90 -30 = TSM
TSM = 60
5. A square has equal sides
the cross creates four equal triangles, with equal angles (because it has equal sides).
since all triangle's angles add up to 180
G J H = 180/3
G J H = 60