When two figures are similar, select whether each statement is True or False.

Question

All corresponding angles are congruent True or False?
No corresponding angles are congruent True or False?
All corresponding sides are proportional True or False?
All corresponding sides are congruent True or False?

Answer 1

Here are the answers to each statement regarding similar figures:

1. All corresponding angles are congruent: True
2. No corresponding angles are congruent: False
3. All corresponding sides are proportional: True
4. All corresponding sides are congruent: False

In summary, similar figures have congruent corresponding angles and proportional corresponding sides, but not necessarily congruent sides unless the figures are also congruent.

Answer 2

complete the proportion.

d/c = c/?

Answer 3

To complete the proportion \( \frac{d}{c} = \frac{c}{?} \), you can use cross-multiplication.

Using the known relationship \( \frac{a}{b} = \frac{c}{d} \), we cross-multiply:

\[ d \cdot ? = c \cdot c \]

This leads to:

\[ d \cdot ? = c^2 \]

To isolate the missing value, we divide both sides by \( d \):

\[ ? = \frac{c^2}{d} \]

Therefore, the completed proportion is:

\[ \frac{d}{c} = \frac{c}{\frac{c^2}{d}} \]

So the missing value is \( \frac{c^2}{d} \).

Answer 4

In ABC, G is the midpoint of AB, H is the midpoint of BC, and I is the midpoint of AC. complete each statement to identify the three pairs of parallel segments.

HI || ??
?? || BC
GH || ??
angle b is 55 degrees and angle a is 35 degrees

if HI = 4 and CB = 10, identify the measure of the following segments:

AG =

AB =

GI =

AC =

Answer 5

To solve the first part of your question regarding the identification of parallel segments in triangle ABC with midpoints G, H, and I, we use the properties of midsegments in triangles. The midsegments connect the midpoints of two sides of a triangle and are parallel to the third side.

1. HI || AC (HI is the midsegment connecting midpoints H and I, and it is parallel to side AC)
2. GH || AC (GH is the midsegment connecting midpoints G and H, and it is parallel to side AC)
3. GH || BC (GH is the midsegment connecting G and H, and it is parallel to side BC)

Now to reflect the segments correctly, we have:

• HI || AC
• GH || BC
• HI || AC

Next, let's calculate the lengths of the segments based on the given information.

Given:

• \( HI = 4 \)
• \( BC = 10 \)

Since \( HI \) is the midsegment joining the midpoints of sides AB and AC, it is equal to half of the length of side BC: \[ HI = \frac{BC}{2} \] Given \( BC = 10 \): \[ HI = \frac{10}{2} = 5 \]

This matches because we were originally given \( HI = 4 \), which will guide us in computing the missing respective sides uniquely.

To find the lengths of the other segments:

1. AG = AB/2: Since G is the midpoint of AB.
2. AC = AB = 10: Since angle B = 55 degrees and A = 35 degrees, typically this implies an isosceles triangle in proportion (values equal rectangle across triangle amends).
3. GI = AG/2 for proportionate segments.

Calculating:

1. From \( HI = 4 \), we find real value \( AC \):

   • \( BC = 10 \to AC = 10 \), \( AB = 5 \times 2 \) (since both angles correspond to it being bisected).

2. Each segment length is half:

   • \( AG = 5 \)
   • \( AC = 10 \)
   • \( GI = 2 \)

Conclusion:

• AG = 5
• AB = 10
• GI = 2
• AC = 10

Let me know if you need any additional information!