1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sdas [7]
3 years ago
11

In ΔABC (m∠C = 90°), the points D and E are the points where the angle bisectors of ∠A and ∠B intersect respectively sides BC an

d AC . Point G ∈ AB so that DG ⊥ AB and H ∈ AB so that EH ⊥ AB .Prove m∠HCG = 45° (with statement reason preferably).
Mathematics
1 answer:
Airida [17]3 years ago
5 0

This is a little long, but it gets you there.

  1. ΔEBH ≅ ΔEBC . . . . HA theorem
  2. EH ≅ EC . . . . . . . . . CPCTC
  3. ∠ECH ≅ ∠EHC . . . base angles of isosceles ΔEHC
  4. ΔAHE ~ ΔDGB ~ ΔACB . . . . AA similarity
  5. ∠AEH ≅ ∠ABC . . . corresponding angles of similar triangle
  6. ∠AEH = ∠ECH + ∠EHC = 2∠ECH . . . external angle is equal to the sum of opposite internal angles (of ΔECH)
  7. ΔDAC ≅ ΔDAG . . . HA theorem
  8. DC ≅ DG . . . . . . . . . CPCTC
  9. ∠DCG ≅ ∠DGC . . . base angles of isosceles ΔDGC
  10. ∠BDG ≅ ∠BAC . . . .corresponding angles of similar triangles
  11. ∠BDG = ∠DCG + ∠DGC = 2∠DCG . . . external angle is equal to the sum of opposite internal angles (of ΔDCG)
  12. ∠BAC + ∠ACB + ∠ABC = 180° . . . . sum of angles of a triangle
  13. (∠BAC)/2 + (∠ACB)/2 + (∠ABC)/2 = 90° . . . . division property of equality (divide equation of 12 by 2)
  14. ∠DCG + 45° + ∠ECH = 90° . . . . substitute (∠BAC)/2 = (∠BDG)/2 = ∠DCG (from 10 and 11); substitute (∠ABC)/2 = (∠AEH)/2 = ∠ECH (from 5 and 6)
  15. This equation represents the sum of angles at point C: ∠DCG + ∠HCG + ∠ECH = 90°, ∴ ∠HCG = 45° . . . . subtraction property of equality, transitive property of equality. (Subtract ∠DCG+∠ECH from both equations (14 and 15).)
You might be interested in
SOMEONE PLEASE HELP ME ASAP THIS IS ALMOST DUE ILL MARK BRAINLIEST!!!!
makkiz [27]

Answer:

153

Step-by-step explanation:

If the table adds up to 20 and opened toe counts for 45% of the total. then 45% of 340 is 153 !

3 0
2 years ago
Help a bab out please?
Volgvan

Answer:

HI

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Which list of ordered pairs does NOT represent a function? A.(8, 80), (6, 80), (3, 80), (7, 80), (5, 80) B. (7, 80), (6, 60), (5
olga_2 [115]

Answer:

A

Step-by-step explanation:

Because they want you to see the number who is repeating like 80 in the later A is 4 times repeated. I hope it help

3 0
2 years ago
Shelly compared the number of oak trees to the number of maple trees as a part of a study about hardwood trees in a woodlot. She
9966 [12]
There were 72 more maple trees before the bug problem then after because there was 108 maple trees before the bug problem and 36 maple trees after the bug problem
6 0
3 years ago
The expression 2.5a+2b gives the cost (in dollars) for a DVDs and b CDs at a moving sale. a. The cost for 1 DVD is $ and the cos
Mekhanik [1.2K]

Answer/Step-by-step Explanation:

Given:

a = no. of DVDs

b = no. of CDs

Total cost ($) for DVDs and CDs = 2.5a + 2b

a. The cost for 1 DVD = 2.5(a) = 2.5(1) = $2.5

The cost for 1 CD = 2(b) = 2(1) = $2

b. Total cost for 4 DVDs and 4 CDs:

Substitute a = 4, and b = 4 into the equation.

2.5(4) + 2(4)

10 + 8 = 18

Total cost for 4 DVDs and 4 CDs = $18

c. To find out if $20 would be enough to buy 6 DVDs and 3 CDs, substitute a = 6, and b = 3 into the equation. Solve for the total cost to see if it equals $20 or is less than $20. If it's greater than $20, then it won't be enough.

2.5(6) + 2(3)

15 + 6 = 21

6 DVDs and 3 CDs cost more than $20, therefore, $20 is not enough.

5 0
2 years ago
Other questions:
  • Is 124 a prime number or not explain why (u can do division to)
    5·1 answer
  • Find the slope and the y-intercept. PLEASE HELP ASAP
    7·1 answer
  • Which set of sides will make a triangle
    9·1 answer
  • 3.426760 * 10^4 please help
    10·1 answer
  • Please help ASAP.. Pythagoras theorem
    14·1 answer
  • Which value is a simplified form of 3^5 / 3^-5<br> ?
    11·1 answer
  • Is this relation a function? Explain how you know.
    15·1 answer
  • Find the difference. Enter your answer in the box below as a fraction, using
    13·1 answer
  • Radius of a cylinder is 6 inches and the
    9·1 answer
  • If x = a sin α, cos β, y = b sin α.sin β and z = c cos α then (x²/a²) + (y²/b²) + (z²/c²) = ?​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!