Day 76 Bellringer Name - highschoolmathteachers.com fileDay 76 Activity Name _____...

Day 76 Bellringer Name ____________________________________

HighSchoolMathTeachers@2018 Page 1

1. Use the triangle below to answer the questions that follow. 𝑄𝑅 =1

2𝐴𝐵

a) What is the ratio of AQ:QC?

b) What is the ratio of BR:RC?

c) Find the length of QR

2. In the diagram below, ∆𝑀𝑁𝑂 is similar to ∆𝐾𝐿𝑂. 𝑀𝑂 = 12𝑖𝑛, 𝐾𝑂 = 4𝑖𝑛 and 𝐿𝑂 = 6𝑖𝑛.

a) Find the length of KL

b) Find the length of LN

A B

C

𝑄 𝑅

2.6𝑖𝑛

M N

O

K L

9𝑖𝑛



Answer Key Day 76:

1. a) 1:1

b) 1:1

c) 1.3𝑖𝑛

2. a) 3𝑖𝑛

b) 12𝑖𝑛

Day 76 Activity Name ____________________________________


1. Draw a 4𝑖𝑛 long line in the middle of a plane paper.

2. Label this line AB.

3. Using the method of your choice construct a line parallel to and above line AB.

4. Make a mark anywhere above the line you have constructed and label it as C.

5. Using a ruler and a pencil join point C and end A.

6. Using a ruler and a pencil join point C and end B such that you have ∆𝐴𝐵𝐶 and a line parallel

to side AB passing through it.

7. Label the points where the parallel line intersects side AC and BC as Q and R respectively.

8. Using a ruler measure the lengths of AQ, QC, BR and RC and record them in the table below.

Line

AQ QC BR RC

Length

9. The ratios 𝐴𝑄

𝑄𝐶 and

𝐵𝑅

𝑅𝐶. Is 𝐴𝑄

𝑄𝐶=

𝐵𝑅

𝑅𝐶?



In this activity, students will draw a triangle of their choice and a line parallel to one of the sides

then establish the proportionality of the parts of the sides divided by the parallel line.

Students will work in groups of at least three and each group is required to have a pencil, a ruler

a compass and a plain paper.

Answer Keys

Day 76:

1-8. No response

9. Yes

Day 76 Practice Name ____________________________________


Use the figure below to answer questions 1 and 4.

𝐴𝐶 = 11𝑖𝑛, 𝐴𝐷 = 5𝑖𝑛, 𝐴𝐹 = 4𝑖𝑛 and 𝐶𝐸 = 5𝑖𝑛.

1. Find the length of FB

2. Find the length of AB

3. Find the length of EB?

4. Find the length of BC

Use the diagram below to answer questions 5 and 8.

5. Find the length of AK

A B

C

D E

F

12𝑖𝑛

4𝑖𝑛

J 6𝑖𝑛 A K

B

L

C

5in



6. Find the length of JK

7. Find the length of CL

8. Find the length of KL

Use the figure below to answer questions 9 and 11.

9. In which ratio does D divide SU?

10. Find the value of x

11. What is the length of side SU?

Use the diagram below to answer questions 12-17. 𝐴𝐺 = 12𝑖𝑛, 𝐺𝐹 = 8𝑖𝑛, 𝐴𝐵 = 8𝑖𝑛, 𝐶𝐷 =9𝑖𝑛, 𝐷𝐸 = 10𝑖𝑛, 𝑂𝐵 = 3𝑖𝑛, 𝑂𝐶 = 2𝑖𝑛 and 𝑂𝐸 = 8𝑖𝑛

12. Find the length of AC

S 2𝑖𝑛 𝐸 4𝑖𝑛 T

D

U

5𝑖𝑛

𝑥

𝐴 𝐵 𝐶 𝐷

G E

F

O



13. Find the length of BC

14. Find the length of AB

15. Find the length of FE?

16. Find the length of DF?

17. Find the length of CG?

Use the diagram below to questions 18 - 19

18. Find the value of 𝑥

19. What is the length of MN?

20. Find the value of y in the figure below.

𝑀 𝑥 𝑅 15𝑖𝑛 𝑁

𝑄

O

24𝑖𝑛

18𝑖𝑛

y

9𝑖𝑛 15𝑖𝑛

3𝑖𝑛



Answer Key

1. 4.8𝑖𝑛

2. 8.8𝑖𝑛

3. 4.17𝑖𝑛

4. 9.17𝑖𝑛

5. 2𝑖𝑛

6. 8𝑖𝑛

7. 15𝑖𝑛

8. 20𝑖𝑛

9. 1:2

10. 2.5𝑖𝑛

11. 7.5 𝑖𝑛

12. 13.5𝑖𝑛

13. 3.375𝑖𝑛

14. 10.125

15. 8.18𝑖𝑛

16. 18.18𝑖𝑛

17. 18𝑖𝑛

18. 11.25𝑖𝑛

19.26.25𝑖𝑛

20.1.8𝑖𝑛

Day 76 Exit Slip Name ____________________________________


Use the diagram below to answer the question that follows.

1. Find the value of 𝑥

𝑥 2.5𝑖𝑛

10𝑖𝑛 8𝑖𝑛



Answer Keys

Day 76:

1. 2𝑖𝑛



Use the figure below to answer the following questions. All length measurements are given in

inches.

1. (a) Identify two triangles similar to ∆ABC.

(b) Identify two triangles that share 𝛼 as one of their angles.

(c) Identify two triangles that share 𝛽 as one of their angles.

2. Using the similar triangles you have identified in the figure above and the ratio of

corresponding sides for proportionality, calculate to two decimal places, the length of the

following sides:

(a) BC

(b) BD

A

B C

D

𝛼

𝛽

16

8

24



Answer keys Day 77:

1. (a) ∆BDC and ∆ADB

(b) ∆ABC and ∆ADB

(c) ∆ABC and ∆BDC

2. (a) BC = 27.71 in.

(b) BD = 13.86 in.



1. Use suitable measurements to construct right ΔABC using a ruler and a protractor on the blank

paper such that ∠BAC = 60°, ∠ABC = 90° and ∠ACB = 30°. ΔABC should appear as shown

below.

2. Drop a perpendicular from point B to intersect AC̅̅̅̅ at point D as shown below.

3. Identify triangles ΔBDC and ΔADB from ΔABC and sketch them on the blank paper. They

should appear as shown below.

A

B C

A

B C

D

A

D B

B

D C



4. Measure ∠ADB and ∠BDC and compare their measures to ∠ABC. What do you notice?

5. Identify two triangles that have ∠A as one of their angles.

6. Identify two triangles that have ∠C as one of their angles.

7. Considering the shapes and sizes of the angles of the triangles above, give the major

relationship between the three triangles above?

8. Measure the lengths AB̅̅ ̅̅ , BC̅̅̅̅ , AD̅̅ ̅̅ , DC̅̅ ̅̅ , BD̅̅ ̅̅ and AC̅̅̅̅ in inches.

9. Find the sum of the squares of the lengths AB̅̅ ̅̅ and BC̅̅̅̅ and compare it to the square of the

length AC̅̅̅̅ on ∠ABC . Write down an identity to show the relationship between the three sides.

10. Find the sum of the squares of the lengths AD̅̅ ̅̅ and BD̅̅ ̅̅ and compare it to the square of the

length AB̅̅ ̅̅ on ∠ADB . Write down an identity to show the relationship between the three sides.

11. Find the sum of the squares of the lengths BD̅̅ ̅̅ and CD̅̅ ̅̅ and compare it to the square of the

length BC̅̅̅̅ on ∠BDC . Write down an identity to show the relationship between the three sides.



In this activity, students will work in groups of four to verify the Pythagoras theorem from

similar right triangles. The students in the respective groups will require a ruler, blank paper, and

a protractor.

Answer keys Day 77:

1. No response

2. No response

3. No response

4. ∠ADB = ∠BDC = ∠ABC = 90°; the three angles are congruent

5. ΔABC and ΔADB

6. ΔABC and ΔBDC

7.The three triangles are similar

8. The lengths should be accurately measured

9. AB̅̅ ̅̅ 2 + BC̅̅̅̅ 2 = AC̅̅̅̅ 2

10. AD̅̅ ̅̅ 2 + BD̅̅ ̅̅ 2 = AB̅̅ ̅̅ 2

11. BD̅̅ ̅̅ 2 + CD̅̅ ̅̅ 2 = BC̅̅̅̅ 2



In the figure 𝑃𝑄 = 𝑟, 𝑄𝑅 = 𝑝, 𝑃𝑅 = 𝑞, 𝑃𝑆 = 𝑛, 𝑅𝑆 = 𝑚 and 𝑄𝑆 ⊥ 𝑃𝑅 at 𝑆 . Study it and use it

to answer questions 1-8 below.

1. Express 𝑞 in terms of 𝑛 and 𝑚.

Given that ∠QPS = 56° and ∠PRQ = 34°. Find the measures of the following angles:

2. ∠QSR

3. ∠SQR

4. ∠PSQ

5. ∠PQS

P

Q R

S

𝑛

𝑚 𝑟

𝑝

𝑞 56°

34°



6. Identify two triangles similar to ΔPQR and label them in such a way that the corresponding

parts match the parts of ΔPQR.

Complete the proportionality statements represented below:

7. 𝑝

=𝑞

𝑝

8. 𝑟

𝑛=

𝑟

Use the proportionality statements in questions 7 and 8 to complete the equations below:

9. 𝑝2 = 𝑞 × ____

10. 𝑟2 = 𝑛 × ____

11. Use the equations in questions 9 and 10 to show that 𝑝2 + 𝑟2 = 𝑞2 by substitution.



In the figure below, ΔABC is a right triangle and BD ⊥ AC. Use it to answer questions 12-20.

Given that ∠CBD = 47° and ∠ABD = 43°. Calculate the measures of the following angles:

12. ∠BCD

13. ∠BAD

14. ∠ADB

15. Write 𝑏 in terms of 𝑥 and 𝑦

Fill in the gaps to complete the proportionality statements below:

16. 𝑎

𝑥=

𝑎 with reference to ΔABC and ΔBDC

A

C B

D

𝑐

𝑦

𝑥

𝑎

𝑏

47°

43°



17. 𝑐

𝑦=

𝑐 with reference to ΔABC and ΔADB

Use the proportionality statements in questions 16 and 17 to complete the equations below:

18. 𝑎2 = 𝑥 × ____

19. 𝑐2 = 𝑦 × ____

20. Use the equations in questions 18 and 19 prove the identity 𝑎2 + 𝑐2 = 𝑏2 by substitution.



Answer keys Day 77:

1. 𝑞 = 𝑚 + 𝑛

2. 90°

3. 56°

4. 90°

5. 34°

6. ΔPSQ and ΔQSR

7. 𝑝

𝑚=

𝑞

𝑝

8. 𝑟

𝑛=

𝑞

𝑟

9. 𝑝2 = 𝑞 × 𝑚

10. 𝑟2 = 𝑛 × 𝑞

11. 𝑝2 + 𝑟2 = 𝑞𝑚 + 𝑞𝑛 = 𝑞(𝑚 + 𝑛) but 𝑚 + 𝑛 = 𝑞 hence 𝑞(𝑚 + 𝑛) = 𝑞 × 𝑞 = 𝑞2

∴ 𝑝2 + 𝑟2 = 𝑞2

12. 43°

13. 47°

14. 90°

15. 𝑏 = 𝑥 + 𝑦

16. 𝑎

𝑥=

𝑏

𝑎

17. 𝑐

𝑦=

𝑏

𝑐

18. 𝑎2 = 𝑥 × 𝑏

19. 𝑐2 = 𝑦 × 𝑏

20. 𝑎2 + 𝑐2 = 𝑏𝑥 + 𝑏𝑦 = 𝑏(𝑥 + 𝑦) but 𝑥 + 𝑦 = 𝑏 hence 𝑏(𝑥 + 𝑦) = 𝑏 × 𝑏 = 𝑏2

∴ 𝑎2 + 𝑐2 = 𝑏2



In the figure 𝐴𝐵 = 𝑐, 𝐵𝐶 = 𝑎, 𝐴𝐶 = 𝑏, 𝐴𝐷 = 𝑥 and 𝐷𝐶 = 𝑦.

(a) Write 𝑏 in terms of 𝑥 and 𝑦.

(b) Complete the proportionality statement below using the sides on ΔABC and ΔADB.

𝑐=

𝑏

𝑐

(c) Complete the proportionality statement below using the sides on ΔABC and ΔBDC.

𝑎=

𝑏

𝑎

A

B C

D

𝑥

𝑦 𝑐

𝑎

𝑏



Answer keys Day 77:

(a) 𝑏 = 𝑥 + 𝑦

(b) 𝑐

𝑥=

𝑏

𝑐

(c) 𝑎

𝑦=

𝑏

𝑎



1. Use triangles below to answer the questions that follow.

a) Which criterion makes the two triangles similar?

b) Find the value of y

c) Find the value of x

2. Use the diagram below to answer the questions that follow.

a) Which postulate makes the triangles above congruent?

b) Find the value of z

9 𝑖𝑛 3 𝑖𝑛

15 𝑖𝑛 12 𝑖𝑛

𝑥 𝑦

(3𝑧 − 2) 𝑖𝑛

7 𝑖𝑛



Answer Key Day 78:

1. a) AA criterion

b) 5 𝑖𝑛

c) 4 𝑖𝑛

2 a) A.S.A postulate

b) 3



1. Draw a rectangle measuring 6 in by 4 in on a plain paper and label it ABCD as shown.

2. Mark the midpoint of AB and label it as O.

3. Draw a straight line joining point O and C.

4. Join points D and O with a straight line.

5. Measure the lengths of sides DO and OC.

Are they equal?

6. Measure the lengths of AO and OB.

Are they equal?

7. Measure the lengths of AD and CB.

Is ∆𝐴𝐷𝑂 ≅ ∆𝐵𝐶𝑂?

Explain your answer.

D C

A B



In this activity, students will draw different triangles and identify the ones that are congruent.

Students will work in groups of at least three and each group is required to have a ruler, a pencil,

and a plain paper.

Answer Keys

Day 78:

1-4. No response

5. Yes

6. Yes

7. Yes, S.S.S postulate



Use the diagram below to answer the questions 1-3.

1. Find the value of r

2. Find the value of p

3. Find the length of AC

4. A student who is 5ft has a shadow of length 15ft. At the same time, the length of the shadow

of a building was 450 ft. What is the height of the building?

Use the diagram below to answer the questions 5 and 6.

5. Find the value of y

2.4 𝑖𝑛 0.8 𝑖𝑛

𝑦

1.1 𝑖𝑛 𝑧

1.8 𝑖𝑛

𝐴 6 𝑖𝑛 𝐵 𝑟 𝐶

3 𝑖𝑛

12 𝑖𝑛

𝑝

9 𝑖𝑛

E

D



6. Find the value of z

Use the diagram below to answer questions 7-11.

𝑀𝑁 = 12𝑖𝑛.

7. Find the value of 𝑥.

8. Find the value of 𝑡

9. Find the value of 𝑦

10. Find the value of s

11. What is the value of w?

12. A mobile phone manufacturing company makes two rectangular models of mobile phones

such that they are similar. The first model has a width of 2 in and a length of 3 in. If the second

model has a width of 2.5 in, what is its length?

A B M N

D E

C O

12 𝑖𝑛

8 𝑖𝑛

10 𝑖𝑛

𝑡 3 𝑖𝑛

𝑠

(5𝑥 + 2) 𝑖𝑛

y 𝑤



Use the figure below to answer questions 13-15.

13. What is the value of 𝑑?

14. Find the value of b

15. Find the value of c

Use the diagram below to answer questions 16 to 20.

The two triangles are image and pre-image of one another under glide reflection.

16. What is the value of 𝑗?

(2𝑏 − 2)

(4𝑐) 𝑖𝑛

10 𝑖𝑛

6 𝑖𝑛

(25 + 2𝑑)°

(3𝑑 − 15)°

2 𝑖𝑛

8 𝑖𝑛

𝑘 1.5 𝑖𝑛

𝑙

9 𝑖𝑛 m

𝑖

𝑗



17. Find the value of 𝑘

18. Find the value of l

19. Find the value of the of m

20. Find the value of 𝑖



Answer Keys

Day 78:

1. 2 𝑖𝑛

2. 3 𝑖𝑛

3. 8 𝑖𝑛

4. 150 𝑓𝑡

5. 3.3 𝑖𝑛

6. 0.6 𝑖𝑛

7. 𝑥 = 2 𝑖𝑛

8. 𝑡 = 5 𝑖𝑛

9. 15 𝑖𝑛

10. 6 𝑖𝑛

11. 9 𝑖𝑛

12. 3.75 𝑖𝑛

13. 40

14. 6

15. 3

2

16. 8 𝑖𝑛

17. 6 𝑖𝑛

18. 3 𝑖𝑛

19. 12 𝑖𝑛

20. 7.5 𝑖𝑛



1. Find the value of 𝑎 in the diagram below.

(𝑎 + 2) 7 𝑖𝑛



Answer Keys Day 78:

1. 5 𝑖𝑛



Use the following diagram to answer the following questions if 𝐺𝑇̅̅ ̅̅ is parallel to 𝐻𝐾̅̅ ̅̅ .

1. Identify two triangles from the diagram above

2. Are the triangles similar or not?

3. Explain your answer.

4. Which condition should the two parallel lines meet for WHKT to be a parallelogram?

5. State the condition that should be met for the two triangles to be congruent.

.

G H

J

K

T



Answer Keys

Day 79:

1. ∆𝑇𝐽𝐺 and ∆𝐾𝐽𝐻

2. Yes

3. Corresponding angles are equal

∠𝑇𝐺𝐽 = ∠𝐾𝐻𝐽(Corresponding angles)

∠𝐽𝑇𝐺 = ∠𝐽𝐾𝐻(Corresponding angles)

∠𝐺𝐽𝑇 = ∠𝐻𝐽𝐾(Common to both triangles)

4. 𝐺𝑇̅̅ ̅̅ = 2𝐻𝐾̅̅ ̅̅ .

5. 𝐺𝑇̅̅ ̅̅ = 𝐻𝐾̅̅ ̅̅ .

G H

J

K

T



1. Draw a rectangle LMNO using a ruler, a pencil and a protractor.

2. Draw a diagonal from L to N.

3. Draw another diagonal from M to O.

4. Label the intersection of the diagonals as P.

5. Measure LM and MO. What do you realize?

6. Measure LP and MP

7. Write a relation between LP and LN.

8. Write a relation between MO and MP.

9. Make a conclusion based on your answer in 8 and 7 above.



In this activity, students will show that the diagonals of a rectangle bisect each other at the point

of intersection. This is taken as a verification of the proof in the presentation. They will work in

groups of at least 3. Each group will require a protractor, a ruler, a pencil and a plain paper.

Answer Keys

Day 79:

1-4. No response

5. Difference responses

They are approximately equal

6. Different responses

7. 2𝐿𝑃 = 𝐿𝑁

8. 2𝑀𝑃 = 𝑀𝑂

9. The diagonals are bisected at the intersection, P.



Use the following information to answer questions 1 – 8

Consider the rhombus below. We want to prove that the diagonals of a rhombus bisects the

angles at their endpoints and intersect at a right angle.

Statement Reason

𝐺𝑆̅̅̅̅ = 𝑆𝑇̅̅̅̅ = 𝑇𝐻̅̅ ̅̅ = 𝐻𝐺̅̅ ̅̅ 1.

In triangle GHT and GST, 𝐺𝑇 = 𝐺𝑇 2.

𝑆𝑇 = 𝐻𝑇, 𝐺𝑆 = 𝐺𝐻, 3.

Triangles GHT and GST are congruent 4.

∠𝐻𝐺𝑇 = ∠𝑆𝐺𝑇, ∠𝐻𝑇𝐺 = ∠𝑆𝑇𝐺 5.

∠𝑆𝑇𝐻 = ∠𝑆𝑇𝐺 + ∠𝐺𝑇𝐻; ∠𝑆𝐺𝐻 = ∠𝑆𝐺𝑇 +

∠𝑇𝐺𝐻

6.

∠𝑆𝑇𝐻 = 2∠𝑆𝑇𝐺 = 2∠𝐺𝑇𝐻; ∠𝑆𝐺𝐻 =

2∠𝑆𝐺𝑇 = 2∠𝑇𝐺𝐻

From 5 and 6 above

Diagonals of a rhombus intersect each other 7.

G H

T S

O



Let ∠𝐺𝑇𝐻 = 𝛼

∠𝐻𝑇𝐺 = ∠𝑆𝑇𝐺 = 𝛼 8.

𝐺𝐻 ∥ 𝑆𝑇 and 𝐺𝑆 ∥ 𝐻𝑇 9.

∠𝐻𝐺𝑇 = ∠𝑆𝑇𝐺 10.

∠𝑆𝑇𝐺 = ∠𝐻𝐺𝑇 = 𝛼; ∠𝐻𝑇𝐺 = ∠𝑆𝑇𝐺 = 𝛼 11.

∠𝑆𝑇𝐻 = 2𝛼; ∠𝑆𝐺𝐻 = 2𝛼 13.

∠𝐺𝑆𝑇 + ∠𝑆𝐺𝐻 = 180° 14.

∠𝐺𝑆𝑇 + 2𝛼 = 180° 15.

∠𝐺𝑆𝑇 = 180° − 2𝛼 16.

∠𝐺𝐻𝑇 = ∠𝐺𝑆𝑇 = 180° − 2𝛼 17.

∠𝐺𝑆𝐻 = ∠𝑇𝑆𝐻 = 90° − 𝛼; ∠𝐺𝐻𝑆 = ∠𝑆𝐻𝑇

= 90° − 𝛼

18.

∠𝐻𝑂𝑇 = ∠𝑇𝑂𝑆 = ∠𝑆𝑂𝐺 = ∠𝐺𝑂𝐻

= 180 − ((90 − 𝛼) + 𝛼)

= 90°

19.

Diagonals of a rhombus intersect at a right

angle

20.



Answer keys Day 79:

Statement Reason

𝐺𝑆̅̅̅̅ = 𝑆𝑇̅̅̅̅ = 𝑇𝐻̅̅ ̅̅ = 𝐻𝐺̅̅ ̅̅ 1. Properties of rhombus

In triangle GHT and GST, 𝐺𝑇 = 𝐺𝑇 2. Common to both triangles

𝑆𝑇 = 𝐻𝑇, 𝐺𝑆 = 𝐺𝐻, 3. By properties of a rhombus

Triangles GHT and GST are congruent 4.Corresponding sides are equal

∠𝐻𝐺𝑇 = ∠𝑆𝐺𝑇, ∠𝐻𝑇𝐺 = ∠𝑆𝑇𝐺 5.Corresponding angles of congruent triangles

∠𝑆𝑇𝐻 = ∠𝑆𝑇𝐺 + ∠𝐺𝑇𝐻; ∠𝑆𝐺𝐻 = ∠𝑆𝐺𝑇 +

∠𝑇𝐺𝐻

6. Sum of Adjacent angles

∠𝑆𝑇𝐻 = 2∠𝑆𝑇𝐺 = 2∠𝐺𝑇𝐻; ∠𝑆𝐺𝐻 =


From 5 and 6 above

Diagonals of a rhombus intersect each other 7.∠𝑆𝑇𝐻 = 2∠𝑆𝑇𝐺 = 2∠𝐺𝑇𝐻; ∠𝑆𝐺𝐻 =




Let ∠𝐺𝑇𝐻 = 𝛼

∠𝐻𝑇𝐺 = ∠𝑆𝑇𝐺 = 𝛼 8.Since ∠𝐻𝑇𝐺 = ∠𝑆𝑇𝐺

𝐺𝐻 ∥ 𝑆𝑇 and 𝐺𝑆 ∥ 𝐻𝑇 9. Properties of rhombus

∠𝐻𝐺𝑇 = ∠𝑆𝑇𝐺 10. Alternate angles

∠𝑆𝑇𝐺 = ∠𝐻𝐺𝑇 = 𝛼; ∠𝐻𝑇𝐺 = ∠𝑆𝑇𝐺 = 𝛼 11. Since ∠𝐻𝐺𝑇 = ∠𝐺𝑇𝑆 and ∠𝐻𝐺𝑇 = 𝛼

Since ∠𝐻𝑇𝐺 = ∠𝑆𝑇𝐺 and ∠𝐻𝑇𝐺 = 𝛼

∠𝑆𝑇𝐻 = 2𝛼; ∠𝑆𝐺𝐻 = 2𝛼 13. ∠𝑆𝑇𝐻 = 2∠𝑆𝑇𝐺 = 2∠𝐺𝑇𝐻; ∠𝑆𝐺𝐻 =


∠𝐺𝑆𝑇 + ∠𝑆𝐺𝐻 = 180° 14. Adjacent angles of a rhombus

∠𝐺𝑆𝑇 + 2𝛼 = 180° 15. Substitution; ∠𝑆𝐺𝐻 = 2𝛼

∠𝐺𝑆𝑇 = 180° − 2𝛼 16. Algebraic equality of substitution

∠𝐺𝐻𝑇 = ∠𝐺𝑆𝑇 = 180° − 2𝛼 17. Opposite angles of a rhombus

∠𝐺𝑆𝐻 = ∠𝑇𝑆𝐻 = 90° − 𝛼; ∠𝐺𝐻𝑆 = ∠𝑆𝐻𝑇

= 90° − 𝛼

18. Diagonals of a rhombus intersect each

other

∠𝐻𝑂𝑇 = ∠𝑇𝑂𝑆 = ∠𝑆𝑂𝐺 = ∠𝐺𝑂𝐻

= 180 − ((90 − 𝛼) + 𝛼)

= 90°

19. Interior angles of a triangle

Diagonals of a rhombus intersect at a right

angle

20. ∠𝐻𝑂𝑇 = ∠𝑇𝑂𝑆 = ∠𝑆𝑂𝐺 = ∠𝐺𝑂𝐻 =

90°



Determine if the two triangles in the figure below are similar if angle DFH and HGE are equal.

Explain your answer.

D E

F

G

H



Answer Keys

Day 79

∠𝐷𝐹𝐻 and ∠𝐻𝐺𝐸 are equal (Given)

∠𝐺𝐸𝐻 = ∠𝐹𝐸𝐷 (Common to both triangles)

Thus AA criteria is satisfied showing that they are similar

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