Podcast
Questions and Answers
In Figure 7.31, if $\angle BAC = 40^\circ$ in isosceles triangle ABC, what is the measure of $\angle EBC$, given that BE is an altitude?
In Figure 7.31, if $\angle BAC = 40^\circ$ in isosceles triangle ABC, what is the measure of $\angle EBC$, given that BE is an altitude?
In Figure 7.32, if BE and CF are equal altitudes of triangle ABC, and $\angle A = 50^\circ$, what is the measure of $\angle B$?
In Figure 7.32, if BE and CF are equal altitudes of triangle ABC, and $\angle A = 50^\circ$, what is the measure of $\angle B$?
Referring to Figure 7.33, if $\angle ABC = 65^\circ$ and $\angle DBC = 30^\circ$, what is the measure of $\angle ABD$?
Referring to Figure 7.33, if $\angle ABC = 65^\circ$ and $\angle DBC = 30^\circ$, what is the measure of $\angle ABD$?
In Figure 7.34, if $\angle BAC = 30^\circ$ and AD = AB in isosceles triangle ABC, what is the measure of $\angle BCD$?
In Figure 7.34, if $\angle BAC = 30^\circ$ and AD = AB in isosceles triangle ABC, what is the measure of $\angle BCD$?
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Given Figure 7.33, if $\angle BAC = x$ and $\angle BDC = y$, and ABC and DBC are isosceles triangles, what is the relationship that relates $\angle ABD$ to angles x and y?
Given Figure 7.33, if $\angle BAC = x$ and $\angle BDC = y$, and ABC and DBC are isosceles triangles, what is the relationship that relates $\angle ABD$ to angles x and y?
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Flashcards
Isosceles Triangle
Isosceles Triangle
A triangle with at least two equal sides.
Altitude of a Triangle
Altitude of a Triangle
A perpendicular segment from a vertex to the opposite side.
Prove BE = CF
Prove BE = CF
Show lengths of altitudes are equal in isosceles triangles.
Prove AB = AC
Prove AB = AC
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∠BCD is a right angle
∠BCD is a right angle
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Study Notes
Triangle Properties
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Figure 7.31: Triangle ABC is isosceles with AB = AC. Perpendiculars BE and CF are drawn to sides AC and AB, respectively. Prove BE = CF.
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Figure 7.32: Triangle ABC has perpendiculars BE and CF from vertices B and C, respectively, to sides AC and AB. Prove that AB = AC (triangle is isosceles).
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Figure 7.33: Two isosceles triangles, ABC and DBC, share the same base BC. Prove that angle ABD = angle ACD.
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Figure 7.34: Triangle ABC is isosceles with AB = AC. Extend the side BA to point D such that AD = AB. Prove that angle BCD is a right angle.
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Description
Explore isosceles triangle properties with perpendiculars and shared bases. Prove equality of sides, angles, and right angles using geometric principles. Examples include proving triangle ABC is isosceles, angle ABD = angle ACD, and angle BCD is a right angle.
