Download Summary of Corresponding Parts

Name_________________________________
Geometry Period _____
5-3 Notes
Date______
5-3: Triangle Congruence and Proof Pieces
Learning Goals: What does it mean for 2 triangles to be congruent? What can we infer based on
knowing that 2 triangles are congruent? What important aspects are included in two-column proofs?
Warm-Up
1. From our homework last night…
What are some things you can conclude from the diagrams given? (List at least 3 conclusions)
a. ___________________
b. ___________________
c. ___________________
*Can we conclude that these two triangles are congruent? Why or why not?
*So, if given ΔABC ≅ ΔDEF, we can identify the pairs of congruent corresponding parts.
Corresponding Angles
Corresponding Sides
<A 
̅̅̅̅
𝐴𝐵 
<B 
̅̅̅̅ 
𝐵𝐶
<C 
̅̅̅̅
𝐴𝐶 
ΔABC is congruent
to ΔDEF because
___________________________
Therefore,
__________________________.
___________________________
.
Congruent Triangles are triangles with
______________ corresponding angles and
_______________ _____________ sides.
Summary of Corresponding Parts
Example 1) If given the following picture, what congruence statement (conclusion) can be
made? Justify your answer.
Example 2) Mark the following diagram based on the given information.
Given: FE//AB, ̅̅̅̅̅̅
𝐵𝐶𝐹 and ̅̅̅̅̅̅
𝐴𝐶𝐸 bisect each other at point c.̅̅̅̅̅
𝐹𝐸 ≅ ̅̅̅̅
𝐴𝐵 .
Prove: ΔABC ≅ ΔEFC
Let’s work in reverse:
Example 3)
Given: ΔABC ≅ ΔXYZ
̅̅̅?
How might we prove that ̅̅̅̅
AC≅ ̅XZ
(Hint: what property to do we need to show congruence?)
Name_________________________________
Geometry Period _____
5-3 Practice
Date______
1. Identify all pairs of congruent corresponding parts in the triangles below. Then, write a
congruence statement for the triangles.
Corresponding angles:
Corresponding sides:
Congruence statement:
*Remember- corresponding parts are mapped to each other!
2. Given: ΔABC ≅ ΔXYZ
Justify that <ACB ≅ <XZY.
3. In exercises 5-8, ΔXYZ ≅ ΔMNL. Complete each statement and explain how you got each answer!
a. m<Y = _____________________________
___________________________________
b. m<M = _____________________________
___________________________________
c. m<Z = _____________________________
___________________________________
d. XY = _______________________________________________________________
4. CD bisects AB at P. Prove AP = PB.
5. Given: E is the midpoint of AB.
Prove: ̿̿̿̿
𝐴𝐸 = ̿̿̿̿
𝐸𝐵
6. Find m<1:
a.
7. Given: Isosceles triangle ∆𝐴𝐵𝐶 with altitude AB.
Prove: ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐵𝐷.
b.
Statement
Reason
1.
1. Given
2. AB ≅ BC
2.
3. BD ≅ BD
3.
4. BD is a perpendicular bisector and an
angle bisector.
4. Altitudes coincide with perpendicular
bisectors and angle bisectors in
_____________ triangles.
5. AD ≅ DC
5.
6. BD ⊥ AC
6.
7. ∠BDA and ∠ BDC are right angles
7.
8.
8. All right angles are congruent.
9. ∠𝐴𝐵𝐷 ≅ ∠𝐶𝐵𝐷
9.
10. ∠A ≅ ∠C
10.
11. ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐵𝐷.
12. All corresponding angles are congruent
and all corresponding sides are
congruent.
Name_________________________________
Geometry Period _____
5-3 HW
Date______
8. Identify all pairs of congruent corresponding parts. Then, write a congruence statement for
the triangles.
9. The triangles below are ______________. How do you know/what property did you use?
10. Find x and y in the following traingles. Explain how you got your answers!
11. Given: CD bisects AB.
Prove: AE = EB
12.Applying the Definition of Congruent Triangles
Prove that triangle ADC is congruent to triangle ADB.
̅̅̅̅ is a perpendicular bisector and 𝑨𝑫
̅̅̅̅ is an angle
Given: 𝑨𝑫
bisector. ΔABC is isosceles.