question 10 of 10

a certain triangle has two $45^\circ$ angles. what type of triangle is it?

a. right isosceles
b. acute scalene
c. right scalene
d. acute isosceles

Question

question 10 of 10

a certain triangle has two $45^\circ$ angles. what type of triangle is it?

a. right isosceles
b. acute scalene
c. right scalene
d. acute isosceles

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Isosceles Triangle Theorem", "Special Right Triangles", "45-45-90 Triangle Theorem" ], "new_concepts": [ "Triangle Angle Sum Theorem" ], "current_concepts": [ "Isosceles Triangle Theorem", "Special Right Triangles", "45-45-90 Triangle Theorem", "Triangle Angle Sum Theorem" ] } ## Find the third angle Using the **Triangle Angle Sum Theorem** $$ \begin{aligned} &\text{Let the angles be } A, B, C.\ &A = 45^\circ, \quad B = 45^\circ\ &C = 180^\circ - (45^\circ + 45^\circ) = 90^\circ \end{aligned} $$ ## Classify by angles Using the **Special Right Triangles** and **45-45-90 Triangle Theorem** knowledge points $$ \begin{aligned} &\text{Since } C = 90^\circ, \text{ the triangle is a right triangle.} \end{aligned} $$ ## Classify by sides Using the **Isosceles Triangle Theorem** knowledge point $$ \begin{aligned} &\text{Since } A = B = 45^\circ, \text{ the triangle is isosceles.} \end{aligned} $$

A. Right isosceles

B. Acute scalene

C. Right scalene

D. Acute isosceles

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QUESTION IMAGE

Question

Explanation:

Find the third angle

Classify by angles

Classify by sides

Answer: