ACTIVITY 1: PROVING Triangle Angle Bisector Theorem (TABT) Illustration If: HD bisects AHE, DA AH Then: Then: DE EH Notice: that sides on the numerators are adjacent. The same is true with the denominators. E Proof Prove DA AH DE EH Proof Extend AH to P such that EP | HD. Given A. HD bisects 2 AHE Statements Reasons No. Hints List down the given What happens to the bisected 2. ZAHE? Definition of angle bisector What can you say about HD and EP? By What can you conclude about LADH & Z DEP and Z1& L4? Corresponding angles are congruent. 4.
ACTIVITY 1: PROVING Triangle Angle Bisector Theorem (TABT) Illustration If: HD bisects AHE, DA AH Then: Then: DE EH Notice: that sides on the numerators are adjacent. The same is true with the denominators. E Proof Prove DA AH DE EH Proof Extend AH to P such that EP | HD. Given A. HD bisects 2 AHE Statements Reasons No. Hints List down the given What happens to the bisected 2. ZAHE? Definition of angle bisector What can you say about HD and EP? By What can you conclude about LADH & Z DEP and Z1& L4? Corresponding angles are congruent. 4.
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
![GRADE 9- Learning Module in Mathematict
What Can you conclude albout
22& 23?
Alternate interior angles are
congruent.
What can you say about
23& L4 based on
statements 2. 4. and 5t
Transitive Property
What kind of triangle is
AHEP based on statement 6f
Base angles of isosceles
triangles are congruent.
AHEPis
8.
What can you say about the
Definition of isosceles triangles
sides opposite 24 & Z3
What can you say about
AAIDA AAPE using
AA Sinilarity Theorem
statement 4?
Lising statement 3, write
the proportional lengths of
AAPE
10
Definition of Similar Polygons
AE
All
AD
Use Segment Addition
Postulate for AP and AE
Segment Addition Postulate
11
Al + AP
AD+ DE
Inversion Property of
Proportion
Use Inversion Property of
12
Proportion statement 11.
IP
AD
DE
Decompose the fractions in
13
Principles in the operations of
fractions
AH
AH
AD
AD
statement 12 and simplify.
DE
HP
+]
AIHL
AD
Subtraction Property of
14
Simplify statement 13.
Equality
Use statement 8 in statement
Substitution
15
14.
Symmetric Property of
Equality
Inversion Property of
Proportion
Use symmetric Property in
16
statement 15.
Use Inversion Property in
17
statement 16.
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Transcribed Image Text:GRADE 9- Learning Module in Mathematict
What Can you conclude albout
22& 23?
Alternate interior angles are
congruent.
What can you say about
23& L4 based on
statements 2. 4. and 5t
Transitive Property
What kind of triangle is
AHEP based on statement 6f
Base angles of isosceles
triangles are congruent.
AHEPis
8.
What can you say about the
Definition of isosceles triangles
sides opposite 24 & Z3
What can you say about
AAIDA AAPE using
AA Sinilarity Theorem
statement 4?
Lising statement 3, write
the proportional lengths of
AAPE
10
Definition of Similar Polygons
AE
All
AD
Use Segment Addition
Postulate for AP and AE
Segment Addition Postulate
11
Al + AP
AD+ DE
Inversion Property of
Proportion
Use Inversion Property of
12
Proportion statement 11.
IP
AD
DE
Decompose the fractions in
13
Principles in the operations of
fractions
AH
AH
AD
AD
statement 12 and simplify.
DE
HP
+]
AIHL
AD
Subtraction Property of
14
Simplify statement 13.
Equality
Use statement 8 in statement
Substitution
15
14.
Symmetric Property of
Equality
Inversion Property of
Proportion
Use symmetric Property in
16
statement 15.
Use Inversion Property in
17
statement 16.
un
Transcribed Image Text:ACTIVITY 1: PROVING Triangle Angle Bisector Theorem (TABT)
Illustration.
If:
HD bisects AHE,
HV Va
EH
Then:
Then: DE
Notice: that sides on the numerators
are adjacent. The same is true with the
E
denominators.
Proof
Prove
DA
AH
DE
EH
Proof
Extend AH to P such that
EP || HD
Given
HD bisects 2AHE
Hints
Statements
Reasons
No.
List down the given
What happens to the bisected
2.
ZAHE?
Definition of angle bisector
What can you say about
3
HD and EP?
By
What can you conclude
Corresponding angles are
4.
about ZADH & ZDEP and
congruent.
L1 & 24?
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