what must be true for two triangles to be similar by aa postulate?
a. all corresponding sides are equal
b. the triangles have the same perimeter
c. the areas of the triangles are equal
d. two pairs of corresponding angles are equal

when using aa similarity in coordinate geometry, which of the following tools is commonly used?
a. compass
b. area formula
c. protractor
d. slope formula

in similar triangles, what is true about their corresponding sides?
a. they are proportional
b. they are parallel
c. they are equal
d. they are perpendicular

if △abc ~ △def, which of the following is true?
a. the triangles have equal perimeters
b. ∠a = ∠d, and ∠b = ∠f
c. the ratios of corresponding side lengths are equal
d. ab = de

which mathematical property justifies why two triangles are similar when two angles are congruent?
a. distributive property
b. angle sum property of a triangle
c. transitive property
d. reflexive property

which of the following is not a step in proving triangle similarity using aa?
a. identify two pairs of corresponding angles
b. show that these angles are congruent
c. prove that the triangles are congruent
d. conclude the triangles are similar

what does the aa in aa similarity stand for?
a. angle - angle

Question

what must be true for two triangles to be similar by aa postulate?
a. all corresponding sides are equal
b. the triangles have the same perimeter
c. the areas of the triangles are equal
d. two pairs of corresponding angles are equal

when using aa similarity in coordinate geometry, which of the following tools is commonly used?
a. compass
b. area formula
c. protractor
d. slope formula

in similar triangles, what is true about their corresponding sides?
a. they are proportional
b. they are parallel
c. they are equal
d. they are perpendicular

if △abc ~ △def, which of the following is true?
a. the triangles have equal perimeters
b. ∠a = ∠d, and ∠b = ∠f
c. the ratios of corresponding side lengths are equal
d. ab = de

which mathematical property justifies why two triangles are similar when two angles are congruent?
a. distributive property
b. angle sum property of a triangle
c. transitive property
d. reflexive property

which of the following is not a step in proving triangle similarity using aa?
a. identify two pairs of corresponding angles
b. show that these angles are congruent
c. prove that the triangles are congruent
d. conclude the triangles are similar

what does the aa in aa similarity stand for?
a. angle - angle

Accepted Answer

# 1. What must be true for two triangles to be similar by AA postulate?
## Brief Explanations:
AA (Angle - Angle) similarity postulate states that if two pairs of corresponding angles of two triangles are equal, then the triangles are similar. Options a (all corresponding sides are equal) is for congruent triangles (by SSS - Side - Side - Side congruence), options b (same perimeter) and c (same area) are not requirements for similarity.
# Answer:
d. Two pairs of corresponding angles are equal

# 2. When using AA similarity in coordinate geometry, which of the following tools is commonly used?
## Brief Explanations:
In coordinate - geometry, the slope formula is used to find the slopes of lines. If the slopes of two lines are equal, the lines are parallel. When two lines are parallel, corresponding angles formed by a transversal are equal. A compass is used for drawing circles or arcs (more for construction in non - coordinate settings), the area formula is for calculating area (not directly for similarity in the context of AA similarity postulate), and a protractor is for measuring angles (but in coordinate geometry, slope is a more common analytical tool for showing parallelism which can lead to equal angles).
# Answer:
d. Slope formula

# 3. In similar triangles, what is true about their corresponding sides?
## Brief Explanations:
By the definition of similar triangles, the ratios of their corresponding side lengths are equal (they are proportional). If sides are equal (option c), the triangles are congruent. Parallel (option b) or perpendicular (option d) are properties of lines, not a general property of corresponding sides of similar triangles.
# Answer:
a. They are proportional

# 4. If $\triangle ABC\sim\triangle DEF$, which of the following is true?
## Brief Explanations:
For similar triangles $\triangle ABC\sim\triangle DEF$, the ratios of corresponding side lengths are equal. Option a (equal perimeters) is not a property of similar triangles (perimeters are in the same ratio as the side lengths). Option b: if $\triangle ABC\sim\triangle DEF$, then $\angle A=\angle D$ and $\angle B = \angle E$ (not $\angle B=\angle F$). Option d ($AB = DE$) would imply congruence (if all corresponding sides are equal), but similar triangles only require proportional sides.
# Answer:
c. The ratios of corresponding side lengths are equal

# 5. Which mathematical property justifies why two triangles are similar when two angles are congruent?
## Brief Explanations:
The Angle - Sum Property of a Triangle states that the sum of the interior angles of a triangle is $180^{\circ}$. If two angles of one triangle are congruent to two angles of another triangle, then the third angles must also be congruent (since $180-( \text{sum of two congruent angles})$ is the same for both triangles). The Distributive Property ($a(b + c)=ab+ac$) is an algebraic property, the Transitive Property ($a = b$ and $b = c$ implies $a = c$) and the Reflexive Property ($a=a$) are not relevant to triangle similarity in this context.
# Answer:
b. Angle Sum Property of a Triangle

# 6. Which of the following is NOT a step in proving triangle similarity using AA?
## Brief Explanations:
When proving triangle similarity using AA:
 - Step 1: Identify two pairs of corresponding angles (option a).
 - Step 2: Show that these angles are congruent (option b).
 - Step 3: Conclude the triangles are similar (option d).
Proving that the triangles are congruent (option c) is a different concept (requires more than just two pairs of congruent angles, like SSS, SAS, etc. for congruence).
# Answer:
c. Prove that the triangles are congruent

# 7. What does the AA in AA similarity stand for?
## Brief Explanations:
By the definition of the AA (Angle - Angle) similarity postulate, the AA stands for two pairs of congruent angles.
# Answer:
a. Angle - Angle

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QUESTION IMAGE

Question

Explanation:

1. What must be true for two triangles to be similar by AA postulate?

Answer:

2. When using AA similarity in coordinate geometry, which of the following tools is commonly used?