hw
when you are finished, check the solutions with your teacher.

1. are the two triangles below similar due to aa triangle similarity theorem?

2. are the two triangles below similar due to aa triangle similarity theorem?

3. what should $\angle d$ and $\angle c$ be to make these two triangles similar?

4. what should $\angle f$ and $\angle z$ be to make these two triangles similar?

5. find the value of the variable.

6. find the value of the variable.

Question

hw
when you are finished, check the solutions with your teacher.

1. are the two triangles below similar due to aa triangle similarity theorem?

2. are the two triangles below similar due to aa triangle similarity theorem?

3. what should $\angle d$ and $\angle c$ be to make these two triangles similar?

4. what should $\angle f$ and $\angle z$ be to make these two triangles similar?

5. find the value of the variable.

6. find the value of the variable.

Accepted Answer

{ "quality": "clear", "question_count": 6, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "AA Triangle Similarity Theorem", "Triangle Angle-Sum Theorem", "Proportional Segments in Triangles" ], "new_concepts": [], "current_concepts": [ "AA Triangle Similarity Theorem", "Triangle Angle-Sum Theorem", "Proportional Segments in Triangles" ] } ## Analyze similarity for Question 1 Using the *AA Triangle Similarity Theorem* and *Triangle Angle-Sum Theorem* knowledge points $$ \begin{aligned} &\angle S = 67^\circ, \quad \angle UVW = 67^\circ\ &\text{Since } \angle S = \angle UVW \text{ and } \angle U \text{ is shared by } \triangle STU \text{ and } \triangle VWU:\ &\triangle STU \sim \triangle VWU \quad (\text{by AA Similarity}) \end{aligned} $$ ## Analyze similarity for Question 2 Using the *AA Triangle Similarity Theorem* and *Triangle Angle-Sum Theorem* knowledge points $$ \begin{aligned} &\angle NMP = 40^\circ, \quad \angle NLQ = 45^\circ\ &\text{Since } \angle NMP e \angle NLQ \text{ and } \angle N \text{ is shared}:\ &\text{The triangles are not similar because corresponding angles are not equal.} \end{aligned} $$ ## Solve for angles in Question 3 Using the *AA Triangle Similarity Theorem* and *Triangle Angle-Sum Theorem* knowledge points $$ \begin{aligned} &\angle B = 92^\circ, \quad \angle E = 92^\circ\ &\angle A = 47^\circ \implies \angle D = 47^\circ\ &\angle C = 180^\circ - (92^\circ + 47^\circ) = 41^\circ \implies \angle F = 41^\circ\ &\angle D = 47^\circ, \quad \angle C = 41^\circ \end{aligned} $$ ## Solve for angles in Question 4 Using the *AA Triangle Similarity Theorem* and *Triangle Angle-Sum Theorem* knowledge points $$ \begin{aligned} &\angle H = 55^\circ \implies \angle G = 55^\circ\ &\angle Y = 77^\circ \implies \angle HFG = 77^\circ\ &\angle Z = 180^\circ - (48^\circ + 77^\circ) = 55^\circ\ &\angle F = 180^\circ - (55^\circ + 48^\circ) = 77^\circ\ &\angle F = 77^\circ, \quad \angle Z = 55^\circ \end{aligned} $$ ## Solve for the variable in Question 5 Using the *Proportional Segments in Triangles* knowledge point $$ \begin{aligned} &\frac{10}{p} = \frac{12}{24}\ &12p = 240 \implies p = 20 \end{aligned} $$ ## Solve for the variable in Question 6 Using the *Proportional Segments in Triangles* knowledge point $$ \begin{aligned} &\frac{10}{10 + 15} = \frac{14}{x} \implies \frac{10}{25} = \frac{14}{x}\ &10x = 350 \implies x = 35 \end{aligned} $$ | No. | Answer | |---|---| | 1 | Yes | | 2 | No | | 3 | $\angle D = 47^\circ$, $\angle C = 41^\circ$ | | 4 | $\angle F = 77^\circ$, $\angle Z = 55^\circ$ | | 5 | $p = 20$ | | 6 | $x = 35$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "AA Triangle Similarity Theorem" ] }

No.	Answer
2	No
3	\(\angle D = 47^\circ\), \(\angle C = 41^\circ\)
4	\(\angle F = 77^\circ\), \(\angle Z = 55^\circ\)
5	\(p = 20\)
6	\(x = 35\)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Analyze similarity for Question 1

Analyze similarity for Question 2

Solve for angles in Question 3

Solve for angles in Question 4

Solve for the variable in Question 5

Solve for the variable in Question 6

Answer: