Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
LEARNING TASK A Directions: Write Yes, if the two triangles are congruent and No if not. State the postulate to justify your answer. LEARNING TASK B Direction: Complete the proof. A. Given: JR bisects ZEJI and EJ 11 Prove: AEJR AIJR E R B. Given: MOLE ML and OE bisect each other at D Prove: AMOD ALED Proof: M AA STATEMENTS 1. EJU 2. 3. 4. AEJR AUR STATEMENTS 1. MO LE 2. 3. MD a LD 4. 5. AMOD ALED REASONS 2. Definition of angle bisector 3. Reflexive Property 14. REASONS 1. 2. Given 3. 4. Reflexive Property 5. man's mind, stretched by new ideas, "A may never return to its original dimensions." Oliver Wendell Holmes Jr ASSESSMENT Directions: Read each of the following carefully. Write the letter of the correct answer. For nos. 4-5 For nos. 1-3 Given: FH bisect AT at 1 and FAI LHTI as shown in the figure. Given: OM bisects LM X 1. ZFIA and ZHIT are congruent angles. What relationship exists between them? D. Adjacent angles A. Linear pair C. Vertical angles 2. Which of the following postulate/theorem can be used to prove AFAI AHTI C. ASA Postulate A. SSS Postulate B. AAS Theorem 3. Which of the following reasons is needed to prove that AI TI? A. Definition of midpoint 8. Vertical Angles Theorem D. CPCTC C. Definition of segment bisector 4. What other information is needed to prove that ALOM.a ANOM by SAS Postulate? 8. ZLOM a NOM A ZMLO ZMNO C. LM a NM 5. What other information is needed to prove that ALOM a ANOM by ASA Postulate? C. LM NM 8. LOMNOM A. ZMLO ZMNO "A man's ma may never retur M N E. A reali D. SAS Pa D. LO a D. LO

LEARNING TASK A Directions: Write Yes, if the two triangles are congruent and No if not. State the postulate to justify your answer. LEARNING TASK B Direction: Complete the proof. A. Given: JR bisects ZEJI and EJ 11 Prove: AEJR AIJR E R B. Given: MOLE ML and OE bisect each other at D Prove: AMOD ALED Proof: M AA STATEMENTS 1. EJU 2. 3. 4. AEJR AUR STATEMENTS 1. MO LE 2. 3. MD a LD 4. 5. AMOD ALED REASONS 2. Definition of angle bisector 3. Reflexive Property 14. REASONS 1. 2. Given 3. 4. Reflexive Property 5. man's mind, stretched by new ideas, "A may never return to its original dimensions." Oliver Wendell Holmes Jr ASSESSMENT Directions: Read each of the following carefully. Write the letter of the correct answer. For nos. 4-5 For nos. 1-3 Given: FH bisect AT at 1 and FAI LHTI as shown in the figure. Given: OM bisects LM X 1. ZFIA and ZHIT are congruent angles. What relationship exists between them? D. Adjacent angles A. Linear pair C. Vertical angles 2. Which of the following postulate/theorem can be used to prove AFAI AHTI C. ASA Postulate A. SSS Postulate B. AAS Theorem 3. Which of the following reasons is needed to prove that AI TI? A. Definition of midpoint 8. Vertical Angles Theorem D. CPCTC C. Definition of segment bisector 4. What other information is needed to prove that ALOM.a ANOM by SAS Postulate? 8. ZLOM a NOM A ZMLO ZMNO C. LM a NM 5. What other information is needed to prove that ALOM a ANOM by ASA Postulate? C. LM NM 8. LOMNOM A. ZMLO ZMNO "A man's ma may never retur M N E. A reali D. SAS Pa D. LO a D. LO

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
arter: 3 Week No. 7 usive Dates: May 3-7, 2021 rning Competencies: Proves two triangles are congruent M8GE-Illg-1 (Grade) ( Section) Scores: Written Output: Performance Task: M +M +K Proving two triangles are Congruent CONGRUENT TRIANGLE, SSS THEOREM COGRUENT TRIANGLE SSS THEOREM Topics wing Two Triangies are Congruent Adea of congruence is when two geometric figures are exactly the same size and shape. w will you prove if the two triangles are congruent? can say that two triangles are congruent if their six corresponding parts are equal. However, we can also say that triangles are congruent without showing all corresponding parts and that is by using some postulates. NOT CONGRUENT, Since AY is not an included side between <M and Y, we cannot conclude that the two triangles are congruent. CONGRUENT TRIANGLE. AAS THEOREM A SAS POSTULATE Let us find out how we can apply the Congruence Postulates to prove that two triangles are congruent. Study the examples below: B. o sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then triangles are congruent. Example 1: (SAS POSTULATE) Given: MA = TA, LMAH 2TAH Prove: AMAH a ATAH If OR AN, 20 LA and BO = YA, then AORB ANYA by SAS Postulate. Statement Reasons 1. MA TA 2. ZMAH ZTAH 3. AH AH 4. AMAH ATAH 1. Given 2. Given 3. Reflexive Property 4. SAS Postulate Take Note: In order to use SAS Postulate, we must be able to identify appropriate sides and angle he diagram, 20 is the included angle of sides OR and while ZA is the included angle of sides YA and NA. Example 2: (ASA POSTULATE) 3. ASA Postulate Let's try to prove. Given: R is the midpoint of MY LEMR LCYR Statements Reasons 1. Given If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. 1. ZEMR LCYR 2. Ris the midpoint of MY 2. Given If 20 ZN, OR NY and R Y, then AORB ANYA by ASA Postulate. 3. MR YR 4. ZERM ZCRY 3. Definition of midpoint 4. Vertical Angle Theorem Prove: AERM ACRY Proof: ASA Postulate Included side is the side formed by two given angles. In the diagram, RO is the included side of angles z0 and R while NY is the include side of angles Y and ZN. 5. AERM = ACRY SSS POSTULATE If the three sides of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. Example 3: SSS POSTULATE Given: AR DR,AC DC REASONS 1. Given 2. Reflexive Property 3. SSS Post STATEMENTS If OR NY, RB YA and OR NA, then AORB ANYA by SSS Postulate. 1. AR E DR, AC a DC 2. CR CR Prove: AACR ADCR 3. AACR ADCR Example 4: (AAS Theorem) Given: LAER B LANR RA bisects LERN STATEMENTS REASONS 1. Given if two angles and the side opposite one of the angles in one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. 1. ZAER LANR 2. RA bisects ZERN AAS Theorem 2. Given Prove: AEAR ANAR 3. Definition of Angle 3. LARE LARN 4. Reflexive Propert 4. RA E RA Given the following figures, can SAS or ASA Postulate be used to show that the triangles are congruent? Explain your answer. le: 5. AAS Theorem 5. AEAR ANAR *A man's mind, streto may never returh to its o Oliven "A man's mind, strelched by new ideas, may never retum to its original dimensions Oliver Wendell Holmes Jr
Transcribed Image Text:arter: 3 Week No. 7 usive Dates: May 3-7, 2021 rning Competencies: Proves two triangles are congruent M8GE-Illg-1 (Grade) ( Section) Scores: Written Output: Performance Task: M +M +K Proving two triangles are Congruent CONGRUENT TRIANGLE, SSS THEOREM COGRUENT TRIANGLE SSS THEOREM Topics wing Two Triangies are Congruent Adea of congruence is when two geometric figures are exactly the same size and shape. w will you prove if the two triangles are congruent? can say that two triangles are congruent if their six corresponding parts are equal. However, we can also say that triangles are congruent without showing all corresponding parts and that is by using some postulates. NOT CONGRUENT, Since AY is not an included side between <M and Y, we cannot conclude that the two triangles are congruent. CONGRUENT TRIANGLE. AAS THEOREM A SAS POSTULATE Let us find out how we can apply the Congruence Postulates to prove that two triangles are congruent. Study the examples below: B. o sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then triangles are congruent. Example 1: (SAS POSTULATE) Given: MA = TA, LMAH 2TAH Prove: AMAH a ATAH If OR AN, 20 LA and BO = YA, then AORB ANYA by SAS Postulate. Statement Reasons 1. MA TA 2. ZMAH ZTAH 3. AH AH 4. AMAH ATAH 1. Given 2. Given 3. Reflexive Property 4. SAS Postulate Take Note: In order to use SAS Postulate, we must be able to identify appropriate sides and angle he diagram, 20 is the included angle of sides OR and while ZA is the included angle of sides YA and NA. Example 2: (ASA POSTULATE) 3. ASA Postulate Let's try to prove. Given: R is the midpoint of MY LEMR LCYR Statements Reasons 1. Given If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. 1. ZEMR LCYR 2. Ris the midpoint of MY 2. Given If 20 ZN, OR NY and R Y, then AORB ANYA by ASA Postulate. 3. MR YR 4. ZERM ZCRY 3. Definition of midpoint 4. Vertical Angle Theorem Prove: AERM ACRY Proof: ASA Postulate Included side is the side formed by two given angles. In the diagram, RO is the included side of angles z0 and R while NY is the include side of angles Y and ZN. 5. AERM = ACRY SSS POSTULATE If the three sides of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. Example 3: SSS POSTULATE Given: AR DR,AC DC REASONS 1. Given 2. Reflexive Property 3. SSS Post STATEMENTS If OR NY, RB YA and OR NA, then AORB ANYA by SSS Postulate. 1. AR E DR, AC a DC 2. CR CR Prove: AACR ADCR 3. AACR ADCR Example 4: (AAS Theorem) Given: LAER B LANR RA bisects LERN STATEMENTS REASONS 1. Given if two angles and the side opposite one of the angles in one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. 1. ZAER LANR 2. RA bisects ZERN AAS Theorem 2. Given Prove: AEAR ANAR 3. Definition of Angle 3. LARE LARN 4. Reflexive Propert 4. RA E RA Given the following figures, can SAS or ASA Postulate be used to show that the triangles are congruent? Explain your answer. le: 5. AAS Theorem 5. AEAR ANAR *A man's mind, streto may never returh to its o Oliven "A man's mind, strelched by new ideas, may never retum to its original dimensions Oliver Wendell Holmes Jr
LEARNING TASK A Directions: Write Yes, If the two triangles are congruent and No if not. State the postulate to justify your answer. ASSESSMENT Directions: Read each of the following carefully. Write the letter of the correct answer. For nos. 1-3 Given: FH bisect AT at I and FAI LHTI as shown In the figure. For nos. 4-5 Given: OM bisects ZLM M 1. ZFIA and ZHIT are congruent angles. What relationship exists between them? C. Vertical angles A. Linear pair D. Adjacent angles E. A real number Which of the following postulate/theorem can be used to prove AFAI = AHTI A. SSS Postulate 3. Which of the following reasons is needed to prove that Al a TI? A. Definition of midpoint C. Definition of segment bisector 2. B. AAS Theorem C. ASA Postulate D. SAS Postulate 5. B. Vertical Angles Theorem D. CPСTC LEARNING TASK B Direction: Complete the proof. 4. What other information is needed to prove that. ALOM a ANOM by SAS Postulate? B. ZLOM = LNOM A. ZMLO = MNO C. LM = NM D. LO =NO A. Given: /R bisects ZEJI and EJ IJ STATEMENTS REASONS 5. What other information is needed to prove that ALOM a ANOM by ASA Postulate? B. LOM = 4NOM 1. EJ EU 1. A. ZMLO ZMNO C. LM =NM D. LO = NO 2. Definition of angle bisector 3. Reflexive Property Prove: AEJR a AIJR 2. 3. 4. AEJR = AIUR 14. STATEMENTS REASONS B. Given: MO LE ML and OE bisect each other at D Prove: AMOD = ALED Proof: 1. 1. МО LE 2. 2. Given 3. 3. MD = LD 4. Reflexive Property 4. 5. 5. AMOD = ALED may never return to its Oliver W "A man's mind, stretched by new ideas, may never return to its original dimensions." Oliver Wendell Holmes Jr
Transcribed Image Text:LEARNING TASK A Directions: Write Yes, If the two triangles are congruent and No if not. State the postulate to justify your answer. ASSESSMENT Directions: Read each of the following carefully. Write the letter of the correct answer. For nos. 1-3 Given: FH bisect AT at I and FAI LHTI as shown In the figure. For nos. 4-5 Given: OM bisects ZLM M 1. ZFIA and ZHIT are congruent angles. What relationship exists between them? C. Vertical angles A. Linear pair D. Adjacent angles E. A real number Which of the following postulate/theorem can be used to prove AFAI = AHTI A. SSS Postulate 3. Which of the following reasons is needed to prove that Al a TI? A. Definition of midpoint C. Definition of segment bisector 2. B. AAS Theorem C. ASA Postulate D. SAS Postulate 5. B. Vertical Angles Theorem D. CPСTC LEARNING TASK B Direction: Complete the proof. 4. What other information is needed to prove that. ALOM a ANOM by SAS Postulate? B. ZLOM = LNOM A. ZMLO = MNO C. LM = NM D. LO =NO A. Given: /R bisects ZEJI and EJ IJ STATEMENTS REASONS 5. What other information is needed to prove that ALOM a ANOM by ASA Postulate? B. LOM = 4NOM 1. EJ EU 1. A. ZMLO ZMNO C. LM =NM D. LO = NO 2. Definition of angle bisector 3. Reflexive Property Prove: AEJR a AIJR 2. 3. 4. AEJR = AIUR 14. STATEMENTS REASONS B. Given: MO LE ML and OE bisect each other at D Prove: AMOD = ALED Proof: 1. 1. МО LE 2. 2. Given 3. 3. MD = LD 4. Reflexive Property 4. 5. 5. AMOD = ALED may never return to its Oliver W "A man's mind, stretched by new ideas, may never return to its original dimensions." Oliver Wendell Holmes Jr
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS