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In this lesson, we will learn how to identify isosceles triangles to find a missing angle or side length.

Q1:

Find the values of π₯ and π¦ .

Q2:

In the figure below, given that π΄ π· = π· πΆ = π΄ πΆ , π΄ π΅ = π΅ πΆ , and π β π΄ π΅ πΆ = 5 4 β , determine π β π΅ π΄ π· .

Q3:

In the figure below, given that π΄ π΅ = π΅ πΆ , π΄ π· = πΆ π· , and π β π΅ π΄ π· = 1 0 8 β , find π β π΄ π· πΆ .

Q4:

Find π β π΅ πΈ π΄ and π β πΈ π΄ πΆ .

Q5:

Find π β π΄ π΅ πΆ .

Q6:

Q7:

If β³ π΄ π΅ πΆ has one line of symmetry, and π β π΄ π΅ πΆ = 1 2 8 β , find π β π΄ .

Q8:

In an isosceles triangle π΄ π΅ πΆ , π΄ π΅ = π΄ πΆ , π΅ πΆ = 6 0 c m , π΄ π· is perpendicular to π΅ πΆ and intersecting the segment at π· , and π β π΅ π΄ π· = 2 6 β . Find the length of π΅ π· and π β π΅ .

Q9:

In the figure, determine all possible values of π¦ .

Q10:

Which of the following is true?

Q11:

Is π π΅ πΆ an isosceles triangle?

Q12:

Q13:

Find π β πΆ π΅ π΄ and π β π· π΄ πΆ .

Q14:

Find π β π΅ π΄ πΆ .

Q15:

Find all possible values of π₯ .

Q16:

In the displayed model of a house, what angle does the roof make with the horizontal, given that β³ π΄ πΈ π΅ is isosceles?

Q17:

Find the value of π₯ .

Q18:

Which pair of segments have the same length?

Q19:

Triangle π΄ π΅ πΆ is isosceles, with π β πΆ = 8 0 β . Determine the measures of π₯ and π¦ .

Q20:

Given that π΄ π· = π· πΆ = πΆ π΅ = π΅ π· , find the value of π₯ .

Q21:

Q22:

Find the value of π₯ in the figure below.

Q23:

In the figure, given that π΄ π· = π΄ πΆ = πΆ π΅ and π β π· = 5 2 β , find π β π· π΄ π΅ .

Q24:

Given that π β π΅ = ( 3 π₯ + 5 2 . 5 ) β and π β πΆ = ( 2 π₯ + 5 3 . 5 ) β , find the measures of the angles of β³ π΄ π΅ πΆ .

Q25:

In the following figure, find the value of π₯ .

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