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
erastovalidia [21]
3 years ago
9

Please Help ! Will give brainliest!

Mathematics
1 answer:
sveta [45]3 years ago
3 0

Answer:

D: I and IV only.

Step-by-step explanation:

We can go through each statement and examine its validity.

I) All congruent triangles are similar.

For congruent triangles, all of its corresponding sides and angles are congruent.

Since all angles are congruent, this fulfills the AA Similarity criterion. Thus, I is true.

II) All similar triangles are congruent.

Congruence guarantees similarity, but similarity does not guarantee congruence.

Two triangles need only two congruent angles to guarantee similarity, while two congruent angles does guarantee congruence. II is false.

III) All right triangles are similar.

Triangles are similar through the AA criterion. One angle of a right triangle must be 90, so this leaves 90 for the two remaining angles. Since these two angles can be anything that sum to 90, we are not guaranteed similarity. For example, 20 - 70 - 90 and 30 - 60 - 90 triangles. They are both right triangles, but are not similar. III is false.

IV) All isosceles right triangles are similar.

Again, since we have a right triangle, one angle is 90, which leaves two remaining angles that must sum to 90.

However, since it is isosceles, the two remaining angles must measure the same. Only one solution exists then: both angles must be 45.

Since all angles must be 45 - 45 - 90, it fulfills the AA Criterion. Thus, all isosceles right triangles are similar. IV is true.

The correct statements are I and IV.

You might be interested in
6,13,20,27 based on the pattern what are the next two terms​
notsponge [240]
34, 41 the pattern is +7
5 0
3 years ago
Read 2 more answers
Express .32 as a fraction
nikdorinn [45]

Answer: 8/25

Step-by-step explanation: Using the place value chart, we can see that the decimal 0.32 is thirty-two hundredths so we can write 0.32 as 32/100.

Since 32/100 is not in lowest terms, we divide both the numerator and the denominator by 4 and we get the equivalent fraction 8/25.

This means that 0.32 can be written as the fraction 8/25 which is in lowest terms.

4 0
3 years ago
It was recently estimated that females outnumber males by about three or two. If there are 1770 people in a county, how many of
max2010maxim [7]

GIVEN

1) Females outnumber males by 3 to 2.

2) There are 1770 people in the city.

SOLUTION

Let the number of males be x and the number of females y. Therefore, the total number of people can be written to be:

x+y=1770\text{   -----------(1)}

If there are 3 females for every 2 males, we have that:

\begin{gathered} \frac{y}{3}=\frac{x}{2} \\ \therefore \\ x=\frac{2y}{3}\text{   ----------(2)} \end{gathered}

We can substitute equation (2) into equation (1) and solve for y:

\begin{gathered} \frac{2}{3}y+y=1770 \\ \frac{2y+3y}{3}=1770 \\ 5y=1770\times3 \\ 5y=5310 \end{gathered}

Dividing both sides by 5, we have

y=1062

There are 1062 females in the county.

3 0
1 year ago
Annie is the height shown.
Phoenix [80]

Answer:

Annie's height= 49 cm

Her brother's height= b+ 49

Let the sum be represented as x

x- 49 = b

7 0
2 years ago
Each pair of figures below is similar. Find the lengths of all unknown sides​
lions [1.4K]

Answer:

  a) w = 8; y = 5.25

  b) x = 10; z = 7.2

Step-by-step explanation:

a) Dimensions on the smaller figure are FA/F'A' = 3/4 times those on the larger figure.

  6 = (3/4)w

  w = 24/3 = 8

  y = (3/4)·7 = 21/4 = 5.25

__

b) Dimensions on the smaller figure are ER/E'R' = 9/15 = 3/5 times those on the larger figure.

  6 = (3/5)x

  x = 30/3 = 10

  z = (3/5)12 = 36/5 = 7.2

7 0
3 years ago
Other questions:
  • Simpligy the expression 7(x+7)-3(x+3)
    8·1 answer
  • Using α = .05, what are the critical values for the test statistic? (to 2 decimals) (+ or -
    13·1 answer
  • Tammy rents an apartment close to her school campus. The amount that she spends on rent is given by the equation r = 355m, where
    15·2 answers
  • Which statement is not true
    7·1 answer
  • There is an animal farm where chickens and cows live. All together, there are 84 heads and 210 legs. How many chickens and cows
    12·1 answer
  • The length of a rectangle is six times its width.
    15·1 answer
  • The Burgesses use about 2 gallons of drinking water per day. If each water jug holds 5 gallons , how many jugs of water do they
    6·1 answer
  • PQR is reflected over the x-axis. What are the<br> coordinates of Q.
    6·1 answer
  • Translate the sentence into an equation or formula.
    14·1 answer
  • Christie bought two kids’ meals today for $7.30. Yesterday, she bought three kids’ meals for $10.95. The equation p = km represe
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!