What is the reason for statement 5 in this proof?Given: ΔABC, where AB = BC (view diagram)
Prove: m∠BAC=m∠BCA
Statement
Reason
1. Let ΔABC be an isosceles triangle with
AB = BC.
given
2. Create point D on side AC¯¯¯¯¯ so BD¯¯¯¯¯ bisects
∠ABC.
constructing an angle bisector
3. m∠ABD=m∠CBD
definition of angle bisector
4. BD = BD
Reflexive Property of Equality
5. ΔABD≅ΔCBD
6. m∠BAC=m∠BCA
Corresponding angles of congruent triangles have equal measures.
A. ASA
B. SSS
C. AAS
D. SAS
Answers
You are comparing side AB, angle ABD, and side BD in one triangle to side CB, angle CBD, and side BD in the other triangle. That is, you are comparing a Side, Angle, and Side in each triangle. The SAS postulate is the reason the triangles are congruent.
Answer:
The correct option is D) SAS
Step-by-step explanation:
Consider the provided statement.
SAS Similarity Theorem: If two sides of a triangle are proportional to the two sides of another triangle and the included angle in both are congruent, then the two triangles are similar.
Statement 1: Let ΔABC be an isosceles triangle where AB = BC.
Reason 1: Given
Statement 2: Create point D on so that bisects ∠ABC as shown.
Reason 2: Constructing an angle bisector.
Statement 3: m∠ABD = m∠DBC
Reason 3: Definition of angle bisector
Statement 4: BD = BD
Reason 4: Reflexive Property of Equality
Statement 5: ΔABD ≅ ΔCBD
Reason 5: SAS
Statement 6: m∠BAC = m∠BCA
Reason 6: Corresponding angles of congruent triangles are equal.
From Reflexive Property of Equality we know BD=BD, m∠ABD = m∠DBC definition of angle bisector and AB = BC, which follows the Side angle side (SAS) similarity.
Related Questions
What is 32% of 60 as a decimal.
कम्प्युटरको गति मापन गर्ने एकाइहरूलाई वर्णन गर्नुहोस् ।
your car weighs 7,630 pounds. There is a road safety fee for cars. you fee is $28 plus $0.023 per pound. What is the fee for your car?
2. Polygon KLMN is similar to polygon PQRS. What is the length of QR?A. 16 mB. 9 cmC. 8 cmD. 6 cm
Answers
Using Pythagoras,the distanceof the fox from its den would be 533.26 yards
- Hypotenus = 900 yards
- Adjacent = 725 yards
- Distance from den = opposite
Opposite = √hypotenus² - adjacent²
Distance = √(900)² - (725)²
Distance = √810000 - 525625
Distance = √284375
Distance = 533.26yards
Therefore, the fox is 533.26yards from his den.
Learn more : Opposite = √hypotenus² - adjacent²
Answer:
1,675
Step-by-step explanation:
add it
Answers
Answer: He will need gallons of paint to paint the entire wall.
Step-by-step explanation:
Given : Area to paint = 142.5 square feet
Paint used to paint of the wall =
gallon
Paint used to paint complete 1 wall = gallons
Paint used to paint complete 1 wall gallons
Hence, he will need gallons of paint to paint the entire wall.
What is the area of the circle using π = 3.14?
113.04 in2
452.16 in2
1,017.36 in2
4,069.44 in2
Answers
Answer:
1017.36 in²
Step-by-step explanation:
Information we need to know:
Radius = diameter ÷ 2
Area of circle = πr²
1) Find the radius of the circle
We have to make sure the we are using the radius of the circle instead of the diameter as the formula using the value of r. If we were to use the diameter our answer would be wrong.
- 36 ÷ 2 = 18
2) Find the area
To find area we can distribute the numbers given into the formula...
- 3.14 (π) x 18 (r)² = 1017.36
Hope this helps, have a lovely day! :)
A = 1,017.36 in²
The answer is option C
Step by step solved:
The formula to calculate the area of a circle is
A = πr²,
where A is the area and r is the radius of the circle. In this case, the diameter of the circle is given as 36 inches, so the radius is half of that, which is 18 inches.
Using the value of π as 3.14, we can plug in the values and calculate the area as follows:
A = πr²
A = 3.14 x 18²
A = 3.14 x 324
A = 1,017.36 in²
Therefore, the area of the circle with a diameter of 36 inches using π = 3.14 is 1,017.36 in². The answer is option C
Q2) x^2-16x+64=144
3Q) x^2-2x+1=81
Answers
Answer:
Q2 :) hope this helps!
Step-by-step explanation:
А 3-х
cx - 3
в 3х
Answers
The expression that shows 3 less than x is (c) x - 3
How to determine the expression that shows 3 less than x?
From the question, we have the following parameters that can be used in our computation:
3 less than x
"less than" here means that we use the negative sign
And also x is greater than 3
i.e. x > 3
So, we have
3 less than x = x - 3
Hence, the expression that shows 3 less than x is (c) x - 3
Read more about expressions at
#SPJ3
Answer:
C: x-3
Step-by-step explanation:
3 less go last
x would go first
and less is the minus sign
450
B
E
А
Answers
Answer:
The measure of angle ADE is equal to 62 degrees.
Step-by-step explanation:
Firstly, I want to remind you that the sum of the interior angles in a quadrilateral are 360 degrees. Now, we are given that CD || BA and CB || DA, which means that this quadrilateral is a parallelogram. This is important because we know that the opposite angles in a parallelogram are congruent, which means that angle C is congruent to angle A and angle B is congruent to angle D. Therefore, the measure of angle A is also 73 degrees. Next, we can represent angle D as x, which means that angle B is equal to x, so the sum of angle D and B is 2x. Finally, we can set up an equation where we solve for the value of x, and then subtract it with 45 degrees:
2x + 2(73) = 360
2x + 146 = 360
2x = 214
x = 107 = B = D
Now, we can subtract the measure of angle D with 45 degrees to get the measure of angle ADE:
ADE = 107 - 45
ADE = 62