Module 1 Lesson 26 ­ Quadrilaterals Day 1.notebook

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Lesson 26 Quadrilaterals Day 1

HW

#5-13

Do Now:Do Now on first page of packet

Nov 4­9:19 AM

Module 1 Lesson 26 ­ Quadrilaterals Day 1.notebook

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GivenAE l BD, AE bisects BD, AB ED≅

Perpendicular lines form right angles

All right angles are congruentA bisector divides a segment into two congruent parts

AAS≅AAS

<DCE and <BCE are right angles<DCE≅<BCE

BC≅DC

ΔACB≅ΔECD<A≅<E Corresponding parts of congruent

triangles are congruent

Module 1 Lesson 26 ­ Quadrilaterals Day 1.notebook

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November 04, 2016

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GivenBF l AC, CE l AB, AE≅AF

Perpendicular lines form right angles<AEC and <BFA are right angles

<AEC≅<BFA

<A ≅ <A

ΔACE≅ΔABF

All right angles are congruent

Reflexive Property

AAS≅AAS

Nov 3­9:20 PM

AB≅DC, AB l AD, DC l BC

Given

Perpendicular lines form right angles

All right angles are congruent

Reflexive Property

A triangle with one right angle is a right triangle

<BAD and <DCB are right angles

<BAD≅<DCB

BD ≅ BD

ΔABD and ΔDBC are right triangles

ΔABD≅ΔDBC HL≅HL

Module 1 Lesson 26 ­ Quadrilaterals Day 1.notebook

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In a parallelogram, opposite angles are congruent

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In a parallelogram, consecutive angles are supplementary

Module 1 Lesson 26 ­ Quadrilaterals Day 1.notebook

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In a parallelogram, diagonals bisect each other

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Given

In a parallelogram, opposite sides are congruent

AD≅BC, DC≅BA

AC≅AC Reflexive Property

ΔDAC≅ΔBCA SSS≅SSS

Module 1 Lesson 26 ­ Quadrilaterals Day 1.notebook

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Given

In a rhombus, all sides are congruent

Vertical angles are congruent

In a rhombus, opposite angles are congruent

Subtraction Postulate

DF≅DT

<DTB ≅ <DCB

<RTD ≅ <FCD

<RDT ≅ <FDC

ΔRDT≅ΔFDC ASA≅ASA RD≅DF Corresponding parts of congruent triangles

are congruent

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Given

In a parallelogram, opposite sides are parallel

If parallel lines are cut by a transversal, alternate interior angles are congruent

If parallel lines are cut by a transversal, alternate exterior angles are congruentASA ASA

ABllEF, AE ll BF

<SDE≅<RCB

<DSE≅<CRB

ΔSDE≅ΔRCB

BR≅SE Corresponding parts of congruent triangles are congruent

Module 1 Lesson 26 ­ Quadrilaterals Day 1.notebook

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GivenIn a square, all sides are congruent

OR≅MP

OR≅OR Reflexive Property

<ROM and <PMO are right angles

All angles are 90 degrees

<ROM≅<PMO All right angles are congruent

ΔROM≅ΔPMO ASA≅ASA

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Given

A midpoint divides a segment into two congruent parts

RM≅SM

In a rectangle, all four angles are 90 degrees

In a rectangle, opposite sides are congruent

<MRU and <MST are right angles

<MRU≅<MST All right angles are congruent

RU≅ST

ΔRMU≅ΔSMT SAS≅ΔSAS

UM≅TM Corresponding Parts of congruent triangles are congruent

ΔUMT is an isosceles triangle

An isosceles triangle has two sides congruent