T-Leng Tuition · mugcornersg.com
Total: 30 marksSuggested time: 50 minutes
Name: ______________________________Class: ____________ Date: ____________
Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.
Section A
1In the diagram, AB is parallel to CD, and the straight line EF cuts them at P and Q. Find x. Answer[2]
2In triangle XYZ, XY=XZ. Find x. Answer[2]
3Ali is constructing triangle ABC with AB=6 cm, ∠BAC=65∘ and ∠ABC=55∘. Which of the following is the first step? Answer[2]
4∠ABC and ∠PQR are supplementary angles. Find x. Answer[2]
5(a)State whether a triangle can be constructed with sides of 8 cm, 2 cm and 6 cm.
Answer (a)[1]
(b)State whether triangle ABC can be constructed with AB=6 cm, ∠BAC=100∘ and ∠ABC=80∘. Answer (b)[2]
Section B
6(a)∠ABC and ∠PQR are complementary angles. Find x. Answer (a)[2]
(b)(i)State whether triangle ABC can be constructed with AB=7 cm, ∠BAC=35∘ and ∠ABC=95∘. Answer (b)(i)[2]
(b)(ii)Which set of data fixes exactly one triangle ABC? Answer (b)(ii)[1]
7(a)In the diagram, AB is parallel to CD, and the straight line EF cuts them at P and Q. Find x. Answer (a)[2]
(b)In triangle PQR, PQ=PR. Find x. Answer (b)[2]
(c)In the diagram, the line segments OA, OB and OC meet at the point O. Find x. Answer (c)[2]
8(a)In triangle ABC, AB=AC. Find x. Answer (a)[1]
(b)In the diagram, AB is parallel to CD, and the straight line EF cuts them at P and Q. Find x. Answer (b)[2]
(c)In the diagram, AOB is a straight line. Find x. Answer (c)[2]
(d)(i)Which set of data fixes exactly one triangle ABC? Answer (d)(i)[1]
(d)(ii)Construct triangle ABC with AB=10 cm, ∠BAC=55∘ and ∠ABC=45∘. Measure the length of AC, to the nearest 0.1 cm. Answer (d)(ii)cm[2]
END OF PAPER
Question 1
Answer: x=66[2] x∘+114∘=180∘ (int. ∠s, AB∥CD)x=180−114x=66 Question 2
Answer: x=41 (∠ sum of △)[2] ∠XZY=x∘ (base ∠s of isos. △)x∘+x∘+98∘=180∘2x=82x=41 (∠ sum of △) Question 3
Answer: draw AB[2]
Nothing is drawn yet.1. Draw AB=6 cm with a ruler. (next)2. At A, measure ∠BAC=65∘ with a protractor and draw a ray.3. At B, measure ∠ABC=55∘ with a protractor and draw a ray.4. Mark C where the two rays cross. Question 4
Answer: x=97 (supplementary ∠s)[2] x∘+83∘=180∘x=180−83x=97 (supplementary ∠s) Question 5
(a)Answer: NO[1]
2+6=88 is equal to 8.No: the two shorter sides only reach along the longest one, so the triangle is flat. (b)Answer: NO[2]
100+80=180180∘ is equal to 180∘.No: the rays from A and B never cross. Question 6
(a)Answer: x=38 (complementary ∠s)[2] x∘+52∘=90∘x=90−52x=38 (complementary ∠s) (b)(i)Answer: YES[2]
35+95=130130∘ is less than 180∘.Yes: the third angle is 50∘ and the rays from A and B cross. (b)(ii)Answer: D[1]
C: 3 + 6 is not more than 10, so the sides cannot meet.A: three angles and no length. Triangles of any size have these angles.B: ∠BAC is not between AB and BC. The arc about B can cut the ray from A twice: two different triangles.D: three sides fix one triangle. Question 7
(a)Answer: x=127[2] x∘+53∘=180∘ (int. ∠s, AB∥CD)x=180−53x=127 (b)Answer: x=31 (∠ sum of △)[2] ∠PRQ=x∘ (base ∠s of isos. △)x∘+x∘+118∘=180∘2x=62x=31 (∠ sum of △) (c)Answer: x=138 (∠s at a pt.)[2] 117∘+x∘+105∘=360∘x=360−117−105x=138 (∠s at a pt.) Question 8
(a)Answer: x=65 (base ∠s of isos. △)[1] x=65 (base ∠s of isos. △) (b)Answer: x=138 (∠s on a str. line)[2] ∠DQP=42∘ (corr. ∠s, AB∥CD)x=180−42x=138 (∠s on a str. line) (c)Answer: x=37 (∠s on a str. line)[2] 143∘+x∘=180∘x=180−143x=37 (∠s on a str. line) (d)(i)Answer: D[1]
C: 3 + 6 is not more than 10, so the sides cannot meet.A: three angles and no length. Triangles of any size have these angles.B: ∠BAC is not between AB and BC. The arc about B can cut the ray from A twice: two different triangles.D: three sides fix one triangle. (d)(ii)Answer: AC=7.2 cm (to the nearest 0.1 cm)[2] Draw AB=10 cm.At A, measure ∠BAC=55∘ and draw a ray.At B, measure ∠ABC=45∘ and draw a ray. The rays cross at C.AC=7.2 cm (to the nearest 0.1 cm)