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Similarity of Triangles
Specific Math Topics
"This quiz is on the similarity of triangles and two related theorems: Midpoint Theorem and the Basic Proportionality Theorem. NOTE: Keep a paper and pencil handy and draw diagrams for ALL questions."
15 Points Per Correct Answer - No time limit
All congruent triangles are similar, but not all similar triangles are congruent.
In a triangle ABC, a line is drawn parallel to BC, which cuts AB at D and AC at E.
The ratio of AD:AB is equal to 3:5.
What is the ratio of DE:BC?
Impossible to say
What is the sign which denotes similarity?
In a triangle XYZ, a line 'PQ' is drawn parallel to YZ, cutting XY at P and XZ at Q.
The ratio of XP:XY is 2:3. What is the ratio XQ:QZ?
Impossible to say
If a line divides two sides of a triangle in proportion, then it is parallel to the third side.
The Midpoint Theorem states:
"A line joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half the length of the third side."
So, riddle me this: What is the converse of the Midpoint Theorem?
"If a line is parallel to one side of a triangle and is equal to half the length of the same side, the given line passes through the midpoints of the other two sides."
"If a line passes through the midpoint of one side of a triangle and is parallel to a second side, the given line bisects the third side."
"If a line passes through the midpoint of one side of a triangle, and is equal to half the length of a second side, it bisects the third side."
None of these are the converse.
Enough about sides. Let's talk areas.
You have been given two similar triangles, MNO and DEF. You have to find out the ratios of their areas.
Which of the following formulae can be used to find out the ratio of the areas of the given triangles.
The ratio of the areas of the triangles is equal to the square of the corresponding sides
The ratio of the areas of the triangles is equal to the square of the corresponding medians
All of these can be used to evaluate the ratio of the areas of the triangles
The ratio of the areas of the triangles is equal to the square of the corresponding altitudes
All equilateral triangles are similar.
A given triangle ABC is isosceles. Angle B and angle C are the base angles.
From B, a perpendicular 'BD' is drawn to cut AC at point D. From C, a perpendicular 'CE' is drawn to cut AB at point E.
State which of the following pairs of triangles are similar.
BDC ~ CEB
CDB ~ BCA
BDC ~ AEB
DBC ~ AEC
ABC and PQR are two triangles. If the ratios of all the corresponding sides of the triangles are equal, then ABC ~ PQR.
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Compiled Jun 22 13