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Season 01 • Episode AP10 • Using congruent triangles

0

Using congruent triangles

Season 01

Episode AP10 Time frame 1 period

Prerequisites :

Voabularyandnotionsabouttrianglesandangles.

Objectives :

•

Use ongruent triangles tosolve problems.

Materials :

•

Exerises.

1 – Exercises Whole period

Working by pairs, students have to solve some exerises and hand out a paper to the

(2)

Using congruent triangles

Season 01

Episode AP10 Document Exercises

Exercise 1

Let

ABC

be asalene triangle,with

CBF G

and

ABDE

two squares built outsideof it 1. Deompose the anglesto prove that

∠ CBD = ∠ ABF

.

2. Dedue that

△ BCD

and

△ ABF

are ongruent.

3. Dedue that

AF = DC

.

Exercise 2

Let

d

1

and

d

2

betwo parallellines, with

A

apointon

d

1

and

B

a pointon

d

2

. Let

K

be

the midpoint of the segment

AB

. Through

K

, draw a line

( D )

that intersets

d 1

in

M

and

d

2

in

N

.

1. Prove that the triangles

KAM

and

KBN

are ongruent.

2. Dedue the positionof

K

on

M N

.

Exercise 3

Let

ABC

beasalenetriangle,with

I

themidpointof

BC

.Let

B ′

and

C ′

betheorthogonal projetions of

B

and

C

ontothe median

AI

of the triangle.

1. Prove that the triangles

I BB ′

and

I CC ′

are ongruent.

2. Dedue from the previous question the nature of

BBCC ′

.

Exercise 4

Let

ABCD

be a square with enter

O

and

M

a point on the side

AB

. Let

P

be the intersetion ofthe side

AD

and the line perpendiular to

CM

through

B

.

1. Prove that

∠ DCM = ∠ BM C

and dedue that

∠ BCM = ∠ ABP

.

2. Dedue that the triangles

M CB

and

P BA

are ongruent and that

M B = AP

. 3. Prove that the triangles

OM B

and

OP A

are ongruent.

4. Dedue that

△ P OM

isright-angledand isoseles.

Références

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