Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Similar Triangles Worksheet 1 : 3 ways to Prove ..., Exercises of Analytical Geometry and Calculus

Union Theological Seminary & Presbyterian School of Christian EducationAnalytical Geometry and Calculus

Worksheet 1 : 3 ways to Prove Similar Triangles. Two Triangles can be similar by : IMP : Sides of Similar Triangles are never equal in size (∴ cannot use ...

Typology: Exercises

2021/2022

Uploaded on 09/12/2022

tomseller
tomseller 🇺🇸

4.6

(16)

276 documents

1 / 5

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Similar Triangles
Worksheet 1 : 3 ways to Prove Similar Triangles
Two Triangles can be similar by :
IMP : Sides of Similar Triangles are never equal in size ( cannot use ‘common side’)
Are the following triangles similar or not ? If yes, give reasons for your answers.
AAA
All corresponding angles equal
RRR
Corresponding sides are in the same ratio
RAR
2 Corresponding sides in the same ratio and INCLUDED angle equal.
(a)
(c)
(e)
(b)
(d)
pf3
pf4
pf5

Partial preview of the text

Download Similar Triangles Worksheet 1 : 3 ways to Prove ... and more Exercises Analytical Geometry and Calculus in PDF only on Docsity!

Similar Triangles

Worksheet 1 : 3 ways to Prove Similar Triangles

Two Triangles can be similar by :

IMP : Sides of Similar Triangles are never equal in size (cannot use ‘ common side ’)

Are the following triangles similar or not? If yes, give reasons for your answers.

AAA All corresponding angles equal

RRR Corresponding sides are in the same ratio

RAR 2 Corresponding sides in the same ratio and INCLUDED angle equal.

(a) (c) (e) (b) (d)

Worksheet 2 : Writing Proofs

1. BEC and AED are two straight lines and AB is parallel to CD. Show that  ABE is similar

to  DEC. D

B

E C

A

Ex 2. Show that  ADE and  ABC are similar.

A

3 cm 4 cm

D E

6 cm 8 cm

B C

3. In  PQR, A is the midpoint of PQ and B is the midpoint of PR. Q

a) What is the scale factor of enlargement from APB to PQR?

b) Show that  PQR is similar to  PAB

c) Hence show that QR is parallel to AB

d) If P = 70° and PBA=50°, find PQR A

e) If AB = 6 cm, find QR.

P B R

4. In  ABC, X is a point on AB and Y is a point on AC such that XY is parallel to BC.

a) Show that  AXY and  ABC are similar

b) If AB is twice as long as XB , and AB = 36 cm, find AX.

c) If XY = 27 cm, how long is BC? (^) A Y

X B C

5. (a) JKLM is a trapezium. Explain why ’s JKM and KLM are similar.

(b) Find the length of JK.

P

6.  PQR is a right angled triangle and PM is perpendicular to QR.

a) Prove that  PRQ is similar to  MRP

b) If QR = 12 cm and PR = 6.5 cm, find MR.

Q M R

Answers:

Worksheet 1:

(a) Yes By RAR (b) Yes By RRR (c) Yes By RAR (d) No, sides not in corresponding position (e) Yes By AAA

Worksheet 2:

  1. To Prove:  ABE is similar to  DEC 2. To Prove:  ADE is similar to  ABC Proof: AEB=CED (vert. opp s) ABE=ECD (alt. s) BAE=EDC (alt. s) Proof: DAE=BAC (common ) ADE=ABC (corr. s) AED=ACB (corr. s) Conc: (^) s𝐴𝐵𝐸 𝐷𝐶𝐸 are similar by AAA Conc: (^) s𝐴𝐷𝐸 𝐴𝐵𝐶 are similar by AAA
  2. a) s.f. = 2 4. a) To Prove:  AXY is similar to  ABC b) To Prove:  PQR is similar to  PAB Proof: Conc: XAY=BAC (common ) AXY=ABC (corr. s) AYX=ACB (corr. s) s𝐴 𝐴𝐵𝐶𝑋𝑌 are similar by AAA Proof: QPR=APB (common ) AP is half PQ (given midpoint) PB is half PR (given midpoint) Conc: s𝑃𝑄𝑅 𝑃𝐴𝐵 are similar by RAR c) By similar s ABP = PRQ,  QR is parallel to BP by corr. s b) AX = 10 cm d) 60  c) BC = 5 4 cm e) QR = 12 cm

Worksheet 3 :

  1. a) To Prove:  PQR is similar to  STR 2. i) To Prove:  ABE is similar to  DCE Proof: PRQ=SRT (vert. opp. s) PQR=RST (alt. s) RPQ=RTS (alt. s) Proof: AEB=DEC (vert. opp. s) BAE=EDC (s in same seg.) ABE=ECD (s in same seg.) Conc: (^) s𝑃𝑄𝑅 𝑇𝑆𝑅 are similar by AAA Conc: (^) s𝐴 𝐷𝐶𝐸𝐵𝐸 are similar by AAA b) PQ =10. 5 cm ii) AC = 1 6 + 3 = 19 cm
  2. i) To Prove:  XAB is similar to  XYZ 4. i) To Prove:  ADE is similar to  ABC Proof: AXB=YXZ (common ) XAB=XYZ (corr. s) XBA=XZY (corr. s) Proof: DAE=BAC (common ) ADE=ABC (corr. s) AED=ACB (corr. s) Conc: s𝑋𝐴𝐵 𝑋𝑌𝑍 are similar by AAA Conc: s𝐴 𝐴𝐵𝐷𝐸𝐶 are similar by AAA ii) AB = 3 6 cm ii) BC = 38 cm
  3. a) To Prove:  JKM is similar to  KLM 6. i) To Prove:  PRQ is similar to  MRP Proof: JMK=KLM = 40 (given) JKM=KML (alt. s) MJK=MKL (remaining s in s) Proof: PRQ=PRM (common ) QPR=PMR = 90 (given) PQR=MPR (remaining s in s) Conc: s 𝐾𝑀𝐿𝐽𝐾𝑀 are similar by AAA Conc: s 𝑀𝑃𝑅𝑄𝑅𝑃 are similar by AAA ii) JK = 4.9 cm ii) MR = 3. 52 cm