The image shown has two triangles sharing a vertex:
There are two triangles labeled HJK and MLK with a common vertex K. In triangle HJK, angle JHK is labeled as y, and angle HJK is labeled as 65 degrees. In triangle MLK, angle MLK is labeled as 65 degrees.
What is the measure of ∠KML, and why? (4 points)
y over 2 , because Triangle JHK is congruent to triangle LMK
y + 50 degrees, because Triangle JHK is similar to triangle MLK
115 degrees - y, because Triangle JHK is congruent to triangle LMK
y, because Triangle JHK is similar to triangle LMK
13 answers
The measure of ∠KML is 115 degrees - y, because triangle JHK is congruent to triangle LMK.
Two similar triangles are shown below:
Two triangles are shown. The sides of the triangle on the left are marked 6, 4, 3. The sides of the triangle on the right are marked as 3, 2 and 1.5. For the triangle on the left, the angle between sides marked 4 and 6 is labeled as w, marked by a double arc, and the angle between the sides marked 6 and 3 is labeled as x, marked by a single arc. The third angle is marked by a triple arc. For the triangle on the right, the angle between sides marked 3 and 1.5 is labeled as y and the angle between the sides marked 2 and 3 is labeled as v, marked by a double arc. The angle between the sides 2 and 1.5 is labeled as z, marked by a triple arc, and it is also the angle on the top vertex of this triangle.
Which two sets of angles are corresponding angles? (4 points)
∠w and ∠v; ∠x and ∠y
∠w and ∠y; ∠x and ∠v
∠w and ∠z; ∠x and ∠v
∠w and ∠z; ∠x and ∠y
Two triangles are shown. The sides of the triangle on the left are marked 6, 4, 3. The sides of the triangle on the right are marked as 3, 2 and 1.5. For the triangle on the left, the angle between sides marked 4 and 6 is labeled as w, marked by a double arc, and the angle between the sides marked 6 and 3 is labeled as x, marked by a single arc. The third angle is marked by a triple arc. For the triangle on the right, the angle between sides marked 3 and 1.5 is labeled as y and the angle between the sides marked 2 and 3 is labeled as v, marked by a double arc. The angle between the sides 2 and 1.5 is labeled as z, marked by a triple arc, and it is also the angle on the top vertex of this triangle.
Which two sets of angles are corresponding angles? (4 points)
∠w and ∠v; ∠x and ∠y
∠w and ∠y; ∠x and ∠v
∠w and ∠z; ∠x and ∠v
∠w and ∠z; ∠x and ∠y
The two sets of corresponding angles are ∠w and ∠y, and ∠x and ∠v.
The figure shows two parallel lines AB and DE cut by the transversals AE and BD:
AB and DE are parallel lines, and AE and BD are transversals. The transversals intersect at C. Angle CAB is labeled 1, angle ABC is labeled 2, angle ACB is labeled 3, angle ACE is labeled 4, angle CDE is labeled 6, and angle CED is labeled 5.
Which statement best explains the relationship between Triangle ABC and Triangle EDC ? (4 points)
Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5
Triangle ABC is similar to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
Triangle ABC is congruent to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5
Triangle ABC is congruent to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
AB and DE are parallel lines, and AE and BD are transversals. The transversals intersect at C. Angle CAB is labeled 1, angle ABC is labeled 2, angle ACB is labeled 3, angle ACE is labeled 4, angle CDE is labeled 6, and angle CED is labeled 5.
Which statement best explains the relationship between Triangle ABC and Triangle EDC ? (4 points)
Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5
Triangle ABC is similar to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
Triangle ABC is congruent to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5
Triangle ABC is congruent to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
The statement "Triangle ABC is similar to triangle EDC, because m∠3 = m∠6 and m∠1 = m∠4" best explains the relationship between Triangle ABC and Triangle EDC.
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠n + m∠p
Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected? (4 points)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
Step 3; it should be m∠m + m∠n + m∠o = m∠o + m∠p
Step 2; it should be m∠o − m∠p = 90 degrees (complementary angles)
A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠n + m∠p
Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected? (4 points)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
Step 3; it should be m∠m + m∠n + m∠o = m∠o + m∠p
Step 2; it should be m∠o − m∠p = 90 degrees (complementary angles)
The student first made a mistake in Step 2. It should be m∠p + m∠o = 180 degrees (supplementary angles), not m∠p + m∠o = 180 degrees (adjacent supplementary angles).
Now are you 100% sure these are correct?
I apologize for the mistake in my previous response. Let me correct it.
The correct answer is that the student first made a mistake in Step 3. Step 3 should state that m∠m + m∠n + m∠o = m∠o + m∠p; not m∠m + m∠n + m∠o = m∠n + m∠p. The correction is that m∠m + m∠n + m∠o = m∠o + m∠p. Thank you for pointing that out.
The correct answer is that the student first made a mistake in Step 3. Step 3 should state that m∠m + m∠n + m∠o = m∠o + m∠p; not m∠m + m∠n + m∠o = m∠n + m∠p. The correction is that m∠m + m∠n + m∠o = m∠o + m∠p. Thank you for pointing that out.
Alright, we'll see.
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