SBTP presentation last Jan. 23, 2015 at Molave Hotel

2. GEOMETRY
Fourth Grading

3. CONTENT STANDARD
The learners demonstrates understanding of
the basic concepts of trigonometry.

4. PERFORMANCE STANDARD
The learner is able to apply the concepts of
trigonometric ratios to formulate and solve
real-life problems with precision and
accuracy.

5. COMPETENCY
The learner illustrates law of sines and
cosines. (M9GE-IVf-g-1)

6. PRE-REQUISITE SKILLS
• Illustrates the six trigonometric ratios: sine,
cosine, tangent, secant, cosecant, and
cotangent. (M9GE-IVa-1)
• Finds the trigonometric ratios of special
angles. (M9GE-IVb-c-1)
• Illustrates the Pythagorean Theorem.

8. ACTIVITY 1
1. What does h
represents in the
∆ABC and what are
its properties?
• h is one of the altitudes ∆ABC.
• It is perpendicular to AB.
• It divides the ∆ABC into two triangles.

9. ACTIVITY 1
2. In ∆ADC, write the
equation that relates
b2 to h2 and x2. Justify
your answer.
By Pythagorean Theorem:
b2 = x2 + h2

10. ACTIVITY 1
3. Write the equation
that relates x to b and
∠A. Justify your
answer.
By trigonometric ratio:
x = b cos A

11. ACTIVITY 1
4. Write the equation
that relates a to h and
c – x in expanded
form.
a2 = h2 + (c – x)2
a2 = h2 + c2 – 2cx + x2

12. ACTIVITY 1
5. Rearrange your
equation such that
the term x2 is next to
the term h2 or vice
versa.
a2 = h2 + c2 – 2cx + x2
a2 = h2 + x2 + c2 – 2cx

13. ACTIVITY 1
6. Underline the part
in your equation in
number 5 which is
similar to your answer
in number 2.
Substitute this
expression into the
expression you wrote
in number 2 and write
it below.
a2 = h2 + x2 + c2 – 2cx
a2 = b2 + c2 – 2cx

14. ACTIVITY 1
7. Substitute x with
your answer in
number 3 and write it
below.
a2 = b2 + c2 – 2cx
a2 = b2 + c2 – 2cb cos A

15. ACTIVITY 2
1. Draw an altitude h
from B. Write the
equation of h in terms
of ∠A and c. Also the
equation of h in terms
of ∠C and a.A
B
C
ac
b
h = c sin A h = a sin C
h

16. ACTIVITY 2
2. Are the two
equations the same?
Justify your answer
and write the equation
that represents the
relationship.A
B
C
ac
b
Yes, since both equations are equal to h.
c sin A = a sin C
h

17. ACTIVITY 2
3. Write your equation
in number 2 in a form
of proportion (fractional
form). What property of
proportion that can
support the process of
rewriting the equation?A
B
C
ac
b
By converse of cross-multiplication property,
h
c sin A = a sin C
c
sin C
=
a
sin A

18. ACTIVITY 2
4. Draw an altitude i
from A. Write the
equation relating i to
∠C and b. Also, write
the equation relating i
to ∠B and c in
fractional form.A
B
C
ac
b
𝑖 =
𝑐
sin C
𝑖 =
𝑏
sin B
h
i

19. ACTIVITY 2
5. Write a new
equation relating the
two equations together.
A
B
C
ac
b
𝑐
sin C
=
𝑏
sin B
h
i

20. ACTIVITY 2
6. Using the Transitive
Property of Equality,
write an equation
relating the equations
in #3 and #5.
A
B
C
ac
b
𝑎
sin A
=
𝑏
sin B
=
𝑐
sin C
h
i