Module 1 Lesson 21 to Lesson 25.notebook

1

November 03, 2016

Oct 31­12:54 PM

Do Now:

On front page of packet

Lessons 21-25 Exploratory Proofs

HWHomework section

#2, 5 & 6

Oct 31­9:07 AM

<E≅<C, B is the midpoint of EC

Given

EB ≅ BC A bisector divides a segment into 2 congruent parts

<EBA ≅<CBA Vertical Angles are congruent

ΔEBA≅ΔCBD ASA ≅ ASA

AE ≅ DC Corresponding parts of congruent triangles are congruent

Module 1 Lesson 21 to Lesson 25.notebook

2

November 03, 2016

Oct 31­9:09 AM

AB≅AC, XB≅XC Given

AX≅AX Reflexive Property

ΔAXB≅ΔAXC SSS ≅ SSS

<BAX ≅<CAX Corresponding parts of congruent triangles are congruent

AX bisects <BAC A bisector divides an angle into two congruent parts

Oct 31­9:09 AM

JX≅JY, KX≅LY Given

<2 ≅ <1 In a triangle, angles opposite congruent sides are congruent

ΔJKX≅ΔJYL

<1 + <3 = 180<2 + <4 = 180

Linear pairs form supplementary angles

<3 ≅ <4 Subtraction Postulate

SAS ≅ SASJK ≅ JL Corresponding parts of congruent

triangles are congruent

ΔJKL is an isosceles triangle

A triangle with two congruent sides in an isosceles triangle

Module 1 Lesson 21 to Lesson 25.notebook

3

November 03, 2016

Oct 31­9:09 AM

GivenΔABC, with XY is the angle bisector of <BYA and BC ll XY

<BYX≅<AYX A bisector divides an angle into two congruent parts

<BYX≅<CBY If parallel lines are cut by a transversal then alternate interior angles are congruent

<BCY≅<AYX If parallel lines are cut by a transversal then corresponding angles are congruent

<AYX≅<CBY<CBY≅<BCY

Substitution

YB≅YC In a triangle, sides opposite congruent angles are congruent.

SKIP

Oct 31­9:09 AM

GivenAB≅BC, AD≅DC

BD≅BD Reflexive Property

ΔADB≅ΔCDB SSS≅SSS

<ADB≅<CDB Corresponding parts of congruent triangles are congruent

<ADB + <CDB = 180 Linear pairs form supplementary angles

<ADB + <ADB = 180Substitution

<ADB = 90

<CDB = 90 Substitution

Subtraction

ΔADB and ΔCDB are right triangles

A triangle with a right angle is a right triangle

Module 1 Lesson 21 to Lesson 25.notebook

4

November 03, 2016

Oct 31­9:09 AM

GivenAC≅AE, BF ll CE

<ACE≅<AEC In a triangle, angles opposite congruent sides are congruent

<ABF≅<ACE<AEC≅<AFB

If parallel lines are cut by a transversal then corresponding angles are congruent

<AEC≅<ABF<ABF≅<AFB

Substitution

AB≅AFIn a triangle, sides opposite congruent angles are congruent