Download Proving Triangles Congruent 17

Proving Triangles Congruent
Lesson 17
Question of the Day: Match the definition with a term from the box. Place the letter in the blank
1.) _______: divides an angle into two congruent adjacent angles
2.) _______: equidistant from the endpoints of a segment, gives two equal pieces of the segment
3.) _______: something is congruent to itself
4.) _______: If two things are congruent to the same thing, then they are congruent.
5.) _______: intersects a segment at its midpoint and forms right angles
6.) _______: angles inside the parallel lines on opposite sides of the transversal
7.) _______: two pairs of corresponding sides and the angle between them are congruent
8.) _______: angles opposite each other when two lines cross
9.) _______: two pairs of corresponding angles and the side next to one of the corresponding angles are
congruent
11.) ______: lines that intersect at right angles
12.) ______: two pairs of corresponding angles and the side between them are congruent
13.) ______: triangle with two congruent sides and its base angles are congruent
14.) ______: corresponding sides of two triangles are congruent
15.) ______: divide into two congruent pieces
16.) ______: Angles on the same location of the parallel lines
17.) ______: pieces of congruent triangles are congruent, used after two triangles are proven congruent
18.) ______: change a congruent symbol of a statement to an equal sign or an equal sign to a congruent
symbol
a.SSS
b. angle bisector
f. AAS g. ASA
c. midpoint
d. SAS
e. vertical angles
h. corresponding parts of congruent triangles are congruent (CPCTC)
k. perpendicular bisector
l. bisect
m. definition of congruence
n. reflexive property
o. alternate interior
p. alternate exterior
q. triangle sum
r. same side interior
s. corresponding angles
t. isosceles triangle
u. perpendicular lines
v. parallel lines
w. transitive property
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Hints to congruency proofs:
1.) If parallel lines are given: look for a __________________________ and find ___________________
2.) If the triangles share a side: it is ______________________ to itself by the ____________________
________________________
3.) If the triangles share a vertex: look for _________________
4.) Must fit one of the four congruence criteria: __________, __________, _____________, or
____________. The parts needed must be proven ___________________ in the proof.
5.) ________________ or bisect: two ________________________ pieces
Introduction to Congruency Proofs: Write a two column proof:
1.)Given: 𝑄𝑃 ≅ 𝑆𝑅, < 𝑃𝑄𝑆 ≅ < 𝑅𝑆𝑄
Prove: ∆𝑃𝑄𝑆 ≅ ∆𝑅𝑆𝑄
2.) Given: 𝐿𝑀 ≅ 𝑃𝑂, 𝐿𝑁 ≅ 𝑃𝑁, N is the
midpoint of MO
Prove: ∆𝑀𝐿𝑁 ≅ ∆𝑂𝑃𝑁
Filling in a Congruency Proof: Fill in the missing statements and reasons
3.)
Given: BA is the perpendicular bisector of RT
Prove: ∆RBA ≅ ∆TBA
Statements
Reasons
1.)
1.)
2.)m<ABT=90; m<ABR=90
2.)
3.)
3.)Transitive Property
4.) < 𝐴𝐵𝑇 ≅< 𝐴𝐵𝑅
4.)
5.)
5.) Def of perpendicular bisector
6.) 𝐵𝐴 ≅ 𝐵𝐴
6.)
7.)
7.)
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4.)
Given: AB ll CD, DB bisects AC
Prove: 𝐸𝐷 ≅ 𝐸𝐵
Statements
Reasons
1.) AB ll CD, DB bisects AC
1.)
2.)
2.) Alternate interior angles
3.) AE ≅ CE
3.)
4.) < 𝐴𝐸𝐵 ≅ < 𝐶𝐸𝐷
4.)
5.) ∆AEB ≅ ∆CED
5.)
6.) 𝐸𝐷 ≅ 𝐸𝐵
6.)
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Independent practice
Lesson 17
W
1.)
T
̅̅̅̅; 𝑇𝐷
̅̅̅̅̅
̅̅̅̅̅ ∥ 𝐷𝑆
̅̅̅̅ ∥ 𝑊𝑆
Given: 𝑇𝑊
Prove: ∆𝑊𝑆𝑇 ≅ ∆𝐷𝑇𝑆
D
S
Statements
Reasons
1.)
1.) Given
2.) < 𝑊𝑇𝑆 ≅< 𝐷𝑆𝑇
2.)
3.) < 𝐷𝑇𝑆 ≅< 𝑊𝑆𝑇
3.)
̅̅̅̅ ≅ 𝑇𝑆
̅̅̅̅
4.) 𝑆𝑇
4.)
5.) ∆𝑊𝑆𝑇 ≅ ∆𝐷𝑇𝑆
5.)
D
A
2.)
Given: X is the midpoint of BD
X is the midpoint of AC
X
C
B
Prove: DA  BC
Statements
Reasons
1. X is the midpoint of BD ; X is the
midpoint of AC .
1.
2.
2. Definition of Midpoint
3. ̅̅̅̅
𝑋𝐷 ≅ ̅̅̅̅
𝑋𝐵
3.
4. < 𝐷𝑋𝐴 ≅< 𝐵𝑋𝐶
4.
5
5. SAS Postulate
6. DA  BC
6.
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